Nathan Roberts, University of Texas at Austin

KAUST-IAMCS Workshop on Multiscale Modeling, Advanced Discretization Techniques, and Simulation of Wave Propagation

May 7-8, 2011

King Abdullah University of Science and Technology (KAUST)

Thuwal, Kingdom of Saudi Arabia

Application of a Discontinuous Petrov-Galerkin Method to the Stokes and Navier-Stokes Equations

Authors: Nathan V. Roberts, Jesse Chan, Leszek D. Demkowicz

The discontinuous Petrov-Galerkin finite element method (DPG) proposed by L. Demkowicz and J. Gopalakrishnan [1] guarantees the optimality of the solution in an energy norm. An important choice that must be made in the application of the method is the denition of the norm on the test space. In this work, we apply the DPG method to the Stokes problem in two dimensions, performing a series of numerical experiments with various test space norms, including one that gives optimal convergence rates. This work extends the work presented in [2]. We will also present initial results from the application of the DPG method to the Navier-Stokes equations in two dimensions.

References:

1. L.D. Demkowicz and J. Gopalakrishnan. A class of discontinuous Petrov-Galerkin methods. II. Optimal test functions. Numerical Methods for Partial Differential Equations, 27:1098-2426, 2010.
2. N.V. Roberts, D. Ridzal, P.B. Bochev, L.D. Demkowicz, K.J. Peterson, and C.M. Siefert. Application of a discontinuous petrov-galerkin method to the stokes equations. Proceedings of the CSRI, pages 32-46, 2010.