A class of discontinuous Petrov-Galerkin methods. Part III

By Leszek F. Demkowicz, Jay Gopalakrishnan, Antti H. Niemi. 2012

210 citations recorded by the source corpus.

We continue our theoretical and numerical study on the Discontinuous Petrov-Galerkin method with optimal test functions in context of 1D and 2D convection-dominated diffusion problems and hp-adaptivity. With a proper choice of the norm for the test space, we prove robustness (uniform stability with respect to the diffusion parameter) and mesh-independence of the energy norm of the FE error for the 1D problem. With hp-adaptivity and a proper scaling of the norms for the test functions, we establish new limits for solving convection-dominated diffusion problems numerically: ?=10-11 for 1D and ?=10-7 for 2D problems. The adaptive process is fully automatic and starts with a mesh consisting of few elements only.

Subfields: Computational Mechanics, Computational Theory and Mathematics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/3bcbb4e5249a752329c404f7c31da8d29032f07a

Citations in the corpus

• A class of discontinuous Petrov–Galerkin methods. II. Optimal test functions (2011, unknown): “Note however that while we solve a symmetric positive definite system for the current DPG method, the first DPG method of [17] obtains the solution by backsubstitution of a block triangular system.”