Bibiliography on A-posteriori
Error Estimation and Superconvergence in Finite Element Analysis
1 I. Babuska and
W. C. Rheinboldt, `A-posteriori error estimates for the
finite element method', Internat. J. Numer. Methods Engrg.,
12, (1978) 1597-1615.
2 I. Babuska and W. C. Rheinboldt, `Adaptive approaches
and reliability estimations in finite element analysis', Comput. Methods
Appl. Engrg., 17/18 , (1979) 519-540.
3 I. Babuska and W. C. Rheinboldt, `Reliable error estimation
and mesh adaptation for the finite element method', in: Computational
Methods in Nonlinear Mechanics, edited by J. T. Oden, North
Holland, Amsterdam, 1980, pp. 67-108.
4 I. Babuska and W. C. Rheinboldt, `A posteriori error
analysis of finite element solutions for one-dimensional problems', SIAM
J. Numer. Anal., 18, (1981) 565-589.
5 I. Babuska and A. Miller, `A-posteriori error estimates and
adaptive techniques for the finite element method', Technical Note BN-968,
Institute for Physical Science and Technology, University of Maryland,
College Park, 1981.
6
D. W. Kelly, J. P. de S.R. Gago, O. C. Zienkiewicz,
and I. Babuska, `A posteriori error analysis and adaptive processes
in the finite element method: Part I-Error analysis', Internat. J.
Numer. Methods Engrg., 19, (1983) 1593-1619.
7
D. W. Kelly, `The self-equilibration of residuals and complementary
a posteriori error estimates in the finite element method', Internat. J.
Numer. Methods Engrg., 20, (1984) 1491-1506.
8
P. Ladeveze, `Comparaison de modeles de milieux continus', These,
Universite P. et M. Curie, Paris, 1975.
9
P. Ladeveze and D. Leguillon, `Error estimate procedure in
the finite element method and applications', SIAM J. Numer. Anal.,
20, (1983) 485-509.
10
R. E. Bank and A. Weiser, `Some a posteriori error estimators
for elliptic partial differential equations', Math. Comp., 44,
(1985) 283-301.
11
I. Babuska and A. Miller, `A feedback finite element method
with a posteriori error estimation: Part I. The finite element method and
some basic properties of the a posteriori error estimator', Comput. Methods Appl. Mech. Engrg.,
61, (1987) 1-40.
12
I. Babuska and D. Yu, `Asymptotically exact a posteriori
error estimator for biquadratic elements', Finite Elements in Analysis
and Design, 3, (1987) 341-354.
13
D. W. Kelly, R. J. Mills, J. A. Reizes
and A. D. Miller, `A posteriori estimates of the solution error
caused by discretization in the finite element, finite difference and boundary
element methods', Internat. J. Numer. Methods Engrg.,
24, (1987) 1921-1939.
14
O. C. Zienkiewicz and J. Z. Zhu, `A simple error
estimator and the adaptive procedure for practical engineering analysis',
Internat. J. Numer. Methods Engrg., 24, (1987) 337-357.
15
E. Rank and O. C. Zienkiewicz, `A simple error estimator
in the finite element method', Comm. Appl. Numer. Methods,
3, (1987) 243-249.
16
M. Ainsworth, J. Z. Zhu, A. W. Craig and O. C. Zienkiewicz,
`Analysis of the Zienkiewicz-Zhu a posteriori error estimator in the finite
element method', Internat. J. Numer. Methods Engrg., 28,
(1989) 2161-2174.
17
J.Z. Zhu and O.C. Zienkiewicz, `Superconvergence recovery technique
and a posteriori error estimators', Internat. J. Numer. Methods Engrg.,
30, (1990) 1321-1339.
18
M. S. Shephard, Q. Niu and P. L. Baehmann,
`Some results using stress projectors for error indication' in: J. E. Flaherty,
P. J. Paslow, M. S. Shephard, J. D. Vasilakis,
eds., Adaptive Methods for Partial Differential Equations SIAM,
Philadelphia, 1989, pp. 83-99.
19
D. W. Kelly and J. D. Isles, `A procedure for a
posteriori error analysis for the finite element method which contains
a bounding measure', Computers & Structures, 31, (1989)
63-71.
20
P. Rougeot, `Sur le controle de la qualite des maillages elements
finis', Ph.D. Thesis, Laboratoire de Mecanique et Technologie, E.N.S
de Cachan-C.N.R.S-Universite Paris 6, Cachan, France (1989).
21
P. Ladeveze, J. P. Pelle and P. Rougeot, `Error
estimation and mesh optimization for classical finite elements', Engineering
Computations, 9, (1991) 69-80.
22
P. Ladeveze, P. Marin, J. P. Pelle and G. L. Gastine,
`Accuracy and optimal meshes in finite element computation for nearly incompressible
materials', Comput. Methods Appl. Mech. Engrg.,
94, (1992) 303-315.
23
C. Johnson and B. Mercier, `Some equilibrium finite element
methods for two-dimensional elasticity problems', Numer. Math.,
30, (1978) 103-116.
24
J. T. Oden, L. Demkowicz, W. Rachowicz and T. A. Westermann,
`Toward a universal h-p adaptive finite element strategy: Part 2, A posteriori
error estimates', Comput. Methods Appl. Mech. Engrg.,
77, (1989) 113-180.
25
T. A. Westermann, `A Posteriori Estimation of Errors in hp
Finite Element Methods for Linear Elliptic Boundary Value Problems', M.Sc. Thesis,
The University of Texas at Austin, Austin, Texas, 1989.
26
K. Eriksson and C. Johnson, `An adaptive finite element method
for linear elliptic problems', Math. Comp., 50, (1988) 361-383.
27
C. Johnson and P. Hansbo, `Adaptive finite element methods
in computational mechanics', Comput. Methods Appl. Mech. Engrg.,
101, (1992) 143-181.
28
R. Verfürth, `A posteriori error estimators for the Stokes
equation', Numer. Math., 55, (1989) 309-325.
29
R. Verfürth, `A posteriori error estimation and adaptive
mesh refinement techniques', preprint, 1992.
30
J. Baranger and H. El-Amri, `Estimateurs a posteriori d'
erreur pour le calcul adaptatifd' ecoulements quasi-newtoniens', RAIRO
Math. Model. Numer. Anal., 25, (1991) 31-48.
31
R. E. Bank and B. D. Welfert, `A posteriori error
estimates for the Stokes equations: A comparison', Comput. Methods
Appl. Mech. Engrg., 82, (1990) 323-340.
32
R. E. Bank and R. K. Smith, `A posteriori error
estimates based on hierarchical bases', preprint, 1992.
33
T. Strouboulis and K. A. Haque, `Recent experiences
with error estimation and adaptivity, Part I: Review of error estimators
for scalar elliptic problems', Comput. Methods Appl. Mech. Engrg.,
97, (1992) 399-436.
34
T. Strouboulis and K. A. Haque, `Recent experiences
with error estimation and adaptivity, Part II: Error estimation for h-adaptive
approximations on grids of triangles and quadrilaterals,' Comput. Methods
Appl. Mech. Engrg., 100, (1992) 359-430.
35
M. Ainsworth and A. Craig, `A posteriori error estimators
in the finite element method', Numer. Math., 60, (1992)
429-463.
36
H. Ohtsubo and M. Kitamura, `Element by element a posteriori
error estimation and improvement of stress solutions for two-dimensional
elastic problems', Internat. J. Numer. Methods Engrg.,
29, (1990) 223-244.
37
H. Ohtsubo and M. Kitamura, `Numerical investigation of elementwise
a-posteriori error estimation in two and three dimensional elastic problems',
Internat. J. Numer. Methods Engrg., 34, (1992)
969-977.
38
H. Ohtsubo and M. Kitamura, `Element by element a posteriori
error estimation of the finite element analysis for three-dimensional elastic
problems', Internat. J. Numer. Methods Engrg., 33,
(1992) 1755-1769.
39
M. Ainsworth and J. .T. Oden, `A procedure for a posteriori
error estimation for h-p finite element methods', Comput. Methods
Appl. Mech. Engrg., 101, (1992) 73-96.
40
M. Ainsworth and J. T. Oden, `A unified approach to
a-posteriori error estimation using element residual methods', Numer.
Math., 65, (1993) 23-50.
41
M. Ainsworth and J. T. Oden, `A posteriori error estimation
for second order elliptic systems. Part 2: An optimal order process for
calculating self equilibrating fluxes,' Comput. Math. Appl., 26,(1993)
75-87.
42
M. Ainsworth, `The performance of the Bank-Weiser's error estimator
for quadrilateral finite elements', Numer. Meth. PDE, 10,
(1994) 609-623.
43
M. Ainsworth and J. T. Oden, `A posteriori error estimation
in finite element analysis', Mathematics and Computer Science Technical
Reports, 1995/14, University of Leicester, July 1995.
44
P. L. Baehmann, M. S. Shephard and J. E. Flaherty,
`A posteriori error estimation for triangular and tetrahedral quadratic
elements using interior residuals', Internat. J. Numer. Methods
Engrg., 34, (1992) 979-996.
45
O. C. Zienkiewicz and J. Z. Zhu, `The superconvergence
patch recovery and a posteriori error estimates. Part 1: The recovery technique',
Internat. J. Numer. Methods Engrg., 33, 1331-1364 (1992).
46
O. C. Zienkiewicz and J. Z. Zhu, `The superconvergence
patch recovery and a posteriori error estimates. Part 2: Error estimates
and adaptivity', Internat. J. Numer. Methods Engrg., 33,
1365-1382 (1992).
47
O. C. Zienkiewicz and J. Z. Zhu, `The superconvergent
patch recovery (SPR) and adaptive finite element refinement', Comput.
Methods Appl. Mech. Engrg., 101, (1992) 207-224.
48
O. C. Zienkiewicz, J. Z. Zhu and J. Wu, `Superconvergent
recovery techniques, some further tests', Comm. Appl. Sci. Engrg.,
9, (1993) 251-258.
49
R. Verfürth, `A review of a-posteriori error estimation and
adaptive mesh-refinement techniques, ' Technical Report, Institüt
für Angewandte Mathmatik der Universität Zürich, 1993.
50
N. E. Wiberg and F. Abdulwahab, `A posteriori error
estimation based on superconvergent derivatives and equilibrium', Publ
92:1, Department of Structural Mechanics, Chalmers University of Technology,
1992.
51
N. E Wiberg and F. Abdulwahab, `Patch recovery based
on superconvergent derivatives and equilibrium. Part 2. Error estimates
and adaptivity', Internat. J. Numer. Methods Engrg., 36,
(1993) 2703-2724.
52
X. D. Li and N. E Wiberg, `A posteriori error estimate
by element patch post-processing, adaptive analysis in energy and 
norms', Computers & Structures, 53, (1994) 907-919.
53
N. E. Wiberg, F. Abdulwahab and S. Ziukas, `Enhanced
superconvergent patch recovery incorporation equilibrium and boundary conditions',
Internat. J. Numer. Methods Engrg., 37, (1994) 3417-3440.
54
T. Blacker and T. Belytschko, `Superconvergent patch recovery
with equilibrium and conjoint interpolant enhancements', Internat. J.
Numer. Methods Engrg., 37, (1994) 517-536.
55
J. Robinson, E. A. W. Maunder and A. C. A. Ramsay,
`Some studies of simple error estimators, Part I - The Philosophy', Finite
Element News, Issue No. 4, (1992) 38-42.
56
J. Robinson, E. A. W. Maunder and A. C. A. Ramsay,
`Some studies of simple error estimators, Part II, Problem I - Convergence
characteristics of the error estimators', Finite Element News, Issue
No. 5, (1992) 36-41.
57
R. H. MacNeal, R. L. Harder, `A proposed standard
set of problems to test finite element accuracy', Journal of Finite
Element Analysis and Design, 1, (1985) 3-20.
58
R. Durán, M. A. Muschietti and R. Rodriguez,
`On the asymptotic exactness of the error estimators for linear triangular
elements', Numer. Math., 59, (1991) 107-127.
59
R. Durán, M. A. Muschietti and R. Rodriguez,
`Asymptotically exact error estimators for rectangular finite elements',
SIAM J. Numer. Anal., 29, (1992) 78-88.
60
I. Babuska, R. Durán and R. Rodriguez, `Analysis of
the efficiency of an a-posteriori error estimator for linear triangular
finite elements', SIAM J. Numer. Anal., 29, (1992)
947-964.
61
I. Babuska, L. Plank and R. Rodriguez, `Quality assessment
of the a-posteriori error estimation in finite elements', Finite Elements
in Analysis and Design, 11, (1992) 5-306.
62
I. Babuska, L. Plank and R. Rodriguez, `Basic problems
of a-posteriori err or estimation', Comput. Methods Appl. Mech. Engrg.,
101, (1992) 97-112.
63
I. Babuska and R. Rodriguez, `The problem of the selection
of an a posteriori error indicator based on smoothening techniques', Internat.
J. Numer. Methods Engrg., 36, (1993) 539-567.
64
R. Rodriguez, `Some remarks on Zienkiewicz-Zhu estimator,' Internat. J.
Numer. Methods in PDEs, to appear.
65
I. Babuska, T. Strouboulis and C. S. Upadhyay,
`A model study of the quality of a posteriori error estimators for linear
elliptic problems. Error estimation in the interior of patchwise uniform
grids of triangles', Comput. Methods Appl. Mech. Engrg.,
114, (1994) 307-378.
66
I. Babuska, T. Strouboulis, C. S. Upadhyay, S. K. Gangaraj
and K. Copps, `Validation of a posteriori error estimators by numerical
approach', Internat. J. Numer. Methods Engrg., 37,
(1994) 1073-1123.
67
I. Babuska, T. Strouboulis, C. S. Upadhyay, S. K. Gangaraj
and K. Copps, `An objective criterion for assessing the reliability
of a-posteriori error estimators in finite element computation', IACM
bulletin, 9, (1994) 27-37.
68
I. Babuska, T. Strouboulis, C. S. Upadhyay and
S. K. Gangaraj, `A model study of element residual estimators
for linear elliptic problems: The quality of the estimators in the interior
of meshes of triangles and quadrilaterals', Computers & Structures,
57, (1995) 1009-1028.
69
I. Babuska, T. Strouboulis and C. S. Upadhyay,
`A model study of the quality of a posteriori error estimators for linear
elliptic problems. Error estimation at the boundary of patchwise uniform
grids of triangles', Internat. J. Numer. Methods Engrg.,
accepted.
70
P. G. Ciarlet, `Basic error estimates for elliptic problems',
in: P.G. Ciarlet and J.L. Lions, eds., Handbook of Numerical Anaylsis,
Vol. II, North-Holland, Amsterdam, (1991) 17-351.
71
I. Babuska, T. Strouboulis, C. S. Upadhyay and
S. K. Gangaraj, `Computer-based proof of the existence of superconvergence
points in the finite element method. Superconvergence of the derivatives
in finite element solutions of Laplace's, Poisson's and the elasticity
equations', Numer. Methods for PDEs, 12, (1996) 347-392.
72
I. Hlavácek and M. Krízek, `On a superconvergent
finite element scheme for elliptic systems. III. Optimal interior estimates',
Aplik. Mat., 32, (1987) 276-289.
73
L. B. Wahlbin, `Local behavior in finite element methods',
in P.G. Ciarlet and J.L. Lions, eds., Handbook of Numerical Analysis,
Vol. II, North-Holland, Amsterdam, (1991) 357-522.
74
J. A. Nitsche and A. H. Schatz, `Interior estimates
for Ritz-Galerkin methods', Math. Comp., 28, (1974).
75
A. H. Schatz and L. B. Wahlbin, `Interior maximum
norm estimates for finite element methods', Math. Comp., 31,
(1977).
76
A. H. Schatz and L. B. Wahlbin, `Interior maximum
norm estimates for finite element methods. Part II', Math. Comp.,
64, (1995).
77
I. Babuska, B. A. Szabo and R. L. Actis, `Hierarchic
models for laminated composites', Internat. J. Numer. Methods Engrg.,
33, (1992) 503-535.
78
S .G. Lekhnitskii, Theory of Elasticity of an Anisotropic
Elastic Body, Holden-Day Inc., San Francisco, 1963.
79
I. Babuska, M. Suri, `On locking and robustness in the finite
element method', SIAM J. Numer. Anal. 29, 5,
(1992) 1261-1293.
80
I. Babuska, M. Suri, `Locking effects in the finite element
approximation of elasticity problems', Numer. Math., 62,
(1992) 439-463.
81
L. R. Scott and M. Vogelius, `Conforming finite element
methods for incompressible continua, in: Large Scale Computations in Fluid
Mechanics', Lectures in Applied Mathematics, Vol. 22, Part 2, AMS,
Providence, Rhode Island, (1985) 221-244.
82
L. A. Oganesyan and L. A. Rukhovets, `Study of
the rate of convergence of variational difference schemes for second-order
elliptic equations in a two-dimensional field with a smooth boundary',
U.S.S.R. Comput. Math. and Math. Phys., 9, (1968) 153-183.
83
J. Douglas,Jr. and T. Dupont, `Superconvergence for Galerkin
methods for the two point boundary problem via local projections', Numer. Math.,
21, (1973) 270-278.
84
J. Douglas,Jr., and T. Dupont, `Galerkin approximations for
the two point boundary problem using continuous piecewise polynomial spaces',
Numer. Math., 22, (1974) 99-109.
85
J. Douglas,Jr., T. Dupont, and M. F. Wheeler, `An
estimate and a superconvergence result for a Galerkin method for elliptic
equations based on tensor products of piecewise polynomials', RAIRO
Anal. Numér., 8, (1974) 61-66.
86
T. Dupont, `A unified theory of superconvergence for Galerkin
methods for two-point boundary problems', SIAM J. Numer. Anal.,
13, (1976) 362-368.
87
J. H. Bramble and A. H. Schatz, `Higher order local
accuracy by averaging in the finite element method', Math. Comp.,
31, (1977) 94-111.
88
V. Thomée, `High order local approximations to derivatives
in the finite element method', Math. Comp., 31, (1977)
652-660.
89
M. Zlámal, `Superconvergence and reduced integration in
the finite element method', Math. Comp., 32, (1978)
663-685.
90
P. Lesaint and M. Zlámal, `Superconvergence of the
gradient of finite element solutions', RAIRO Anal. Numér.,
13, (1979) 139-166.
91
A. Louis, `Acceleration of convergence for finite element solutions
of the Poisson equation', Numer. Math., 33, (1979) 43-53.
92
I. Babuska and A. Miller, `The post-processing approach in
the finite element method. Part 1: Calculation of displacements, stresses
and other higher derivatives of the displacements', Internat. J. Numer.
Methods Engrg., 20, (1984) 1085-1109.
93
I. Babuska, K. Izadpanah and B. Szabo, `The postprocessing
technique in the finite element method. The theory and experience', in
Unification of Finite Element Methods, H. Kardestuncer, Ed., Elsevier
Science Publishers B.V., (1984) 97-121.
94
M. Krizek and P. Neitaanmäki, `Superconvergence phenomenon
in the finite element method arising from averaging gradients', Numer. Math.,
45, (1984) 105-116.
95
N. Levine, `Superconvergent recovery of the gradient from piecewise
linear finite element approximations', IMA J. Numer. Anal., 5,
(1985) 407-427.
96
M. F. Wheeler and J. R. Whiteman, `Superconvergent
recovery of gradient on subdomains from piecewise linear finite-element
approximations', Numer. Methods for PDEs, 3, (1987) 65-82.
97
M. Krizek and P. Neitaanmäki, `On superconvergence techniques',
Acta Applic. Math., 9, (1987) 175-198.
98
M. T. Nakao, `Superconvergence of the gradient of Galerkin
approximations for elliptic problems', RAIRO Math. Model. Numer. Anal.,
21, (1987) 679-695.
99
M. T. Nakao, `Superconvergence of the gradient of Galerkin
approximations for elliptic problems', J. Comput. Appl. Math., 20,
(1987) 341-348.
100
M. Krízek and P. Neittaanmäki, `On a global superconvergence
of the gradient of linear triangular elements', J. Comput. Appl. Math.,
18, (1987) 221-233.
101
I. Hlavácek and M. Krízek, `On a superconvergent
finite element scheme for elliptic systems. I. Dirichlet boundary condition',
Aplik. Mat., 32, (1987) 131-154.
102
I. Hlavácek and M. Krízek, `On a superconvergent
finite element scheme for elliptic systems. II. Boundary conditions of
Newton's or Neumann's type', Aplik. Mat., 32, (1987) 200-213.
103
I. Hlavácek, M. Krízek and V. Pistora,
`How to recover the gradient of linear elements on irregular triangulations
?', submitted to IMA J. Numer. Anal..
104
A. B. Andreev and R. D. Lazarov, `Superconvergence
of the gradient for quadratic triangular finite elements', Numer. Methods
for PDEs, 4, (1988) 15-32.
105
W. Rachowicz and J. T. Oden, `On the accuracy and convergence
of conjugate flux approximations', Numer. Methods for PDEs, 5,
(1989) 143-156.
106
Q. D. Zhu and Q. Lin, `Superconvergence theory of FEM',
Hunan Science Press, (1989).
107
G. Goodsell and J. R. Whiteman, `A unified treatment
of superconvergent recovered gradient functions for piecewise linear finite
element approximations', Internat. J. Numer. Methods Engrg., 27,
(1989) 469-481.
108
G. Goodsell and J. R. Whiteman, `Pointwise superconvergence
of recovered gradients for piecewise linear finite element approximations
to problems of planar linear elasticity', Numer. Methods for PDEs,
6, (1990) 59-74.
109
A. H. Schatz, I. H. Sloan and L. B. Wahlbin,
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with respect to a point', SIAM J. Numer. Anal., 33, (1996)
409-434.
110
L. B. Wahlbin, Superconvergence in Galerkin Finite Element
Methods, Lecture Notes in Mathematics, 1605, Springer-Verlag,
New York, 1995.
111
I. Babuska, T. Strouboulis and C. S. Upadhyay,
` 
-superconvergence of finite element approximations in the interior of general
meshes of triangles',Comput. Methods Appl. Mech. Engrg., 122,
(1995) 273-305.
112
I. Babuska, T. Strouboulis, S. K. Gangaraj and
C. S. Upadhyay, `
-superconvergence in the interior of locally refined meshes of quadrilaterals:
Superconvergence of the gradient in finite element solutions of Laplace's
and Poisson's equations', Appl. Numer. Math., 16, (1994)
3-49.
113
I. Babuska, T. Strouboulis, S. K. Gangaraj and
C. S. Upadhyay, `Validation of recipes for the recovery of stresses
and derivatives by a computer-based approach', Mathl. Comput. Modelling,
20, (1994) 45-89.
114
I. Babuska, T. Strouboulis, C. S. Upadhyay and
S. K. Gangaraj, `Superconvergence in the finite element method
by computer-based proof', IACM bulletin, 10, (1995) 27-41.
115
J. T. Oden and H. Brauchli, `On the calculation of consistent
stresses distributions in finite element approximations', Internat.
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E. Hinton and J. S. Campbell, `Local and global smoothing
of discontinuous finite element functions using a least-squares method',
Internat. J. Numer. Methods Engrg., 8, (1974) 461-480.
117
E. Hinton, F. C. Scott and R. E. Ricketts,
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J.B. Ransom and N.F. Knight Jr., `Global/Local analysis for
composite panels', Computers & Structures, 37 (1990)
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M.A. Aminpour, S.L. McCleary, J.B. Ransom and J.M. Housner, `A global/
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121
J. Fish and S. Markofelas, `Adaptive global-local refinement strategy
based on the interior error estimates of the h-method,' Int. J. Numer.
Methods Eng., 37, (1994) 827-838.
122
I. Babuska, T. Strouboulis, A. Mathur and C. S. Upadhyay,
`Pollution-error in the h-version of the finite-element method and the
local quality of a-posteriori error estimators', Finite Elements in
Analysis and Design, 17, (1994) 273-321.
123
I. Babuska, T. Strouboulis , C. S. Upadhyay and
S. K. Gangaraj, `A posteriori estimation and adaptive control
of the pollution error in the h-version of the finite element method',
Internat. J. Numer. Methods Engrg., 38, (1995) 4207-4235.
124
B. A. Szabo and I. Babuska, Finite Element Analysis,
John Wiley & Sons, Inc., New York, 1991.
125
I. Babuska, T. Strouboulis, S. K. Gangaraj and
C. S. Upadhyay, `Pollution error in the h-version of the finite
element method and the local quality of the recovered derivatives', Comput.
Methods Appl. Mech. Engrg., to appear.
126
I. Holand, `The Sleipner accident' in: K. Bell, ed., From Finite
Elements to the Troll Platform, Department of Structural Engineering,
The Norwegian Institute of Technology, Trondheim, Norway, (1994) 157-168.
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128
W.K. Rettedal, O.T. Gudmestad and T. Aarum, `Design of concrete platforms
after Sleipner A-1 sinking' in: S.K. Chakrabarti, C. Agee, H. Maeda, A.N.
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I. Babuska and W. C. Rheinboldt, `Error estimates for
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15, (1978) 736-754.