Paper Info
Title
Robust Adaptive $hp$ Discontinuous Galerkin Finite Element Methods for the Helmholtz Equation
Abstract
This paper presents an hp a posteriori error analysis for the 2D Helmholtz equation that is robust in the polynomial degree p and the wave number k. For the discretization, we consider a discontinuous Galerkin formulation that is unconditionally well posed. The a posteriori error analysis is based on the technique of equilibrated fluxes applied to a shifted Poisson problem, with the error due to the nonconformity of the discretization controlled by a potential reconstruction. We prove that the error estimator is both reliable and efficient, under the condition that the initial mesh size and polynomial degree are chosen such that the discontinuous Galerkin formulation converges, i.e., it is out of the regime of pollution. We confirm the efficiency of an hp-adaptive refinement strategy based on the presented robust a posteriori error estimator via several numerical examples.
Year
DOI
Venue
2019
10.1137/18M1207909
SIAM JOURNAL ON SCIENTIFIC COMPUTING
Keywords
Field
DocType
a posteriori error analysis,hp discontinuous Galerkin finite element method,equilibrated fluxes,potential reconstruction,Helmholtz problem
Discontinuous Galerkin method,Discretization,Mathematical analysis,A priori and a posteriori,Degree of a polynomial,Finite element method,Helmholtz equation,Mathematics
Journal
Volume
Issue
ISSN
41
2
1064-8275
Citations 
PageRank 
References 
0
0.34
0
Authors
3
Name
Order
Citations
PageRank
Scott Congreve131.46
Joscha Gedicke2589.24
Ilaria Perugia3534134.99