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hp non-conforming a priori error analysis of an Interior Penalty Discontinuous Galerkin BEM for the Helmholtz equation.
- Source :
-
Computers & Mathematics with Applications . Dec2020, Vol. 80 Issue 12, p2644-2675. 32p. - Publication Year :
- 2020
-
Abstract
- This work is concerned with the construction and the hp non-conforming a priori error analysis of a Discontinuous Galerkin DG numerical scheme applied to the hypersingular integral equation related to the Helmholtz problem in 3D. The main results of this article are an error bound in a norm suited to the problem and in the L 2 -norm. Those bounds are quasi-optimal for the h -convergence and the p -convergence. Various formulation choices and penalty functions are theoretically discussed. In particular we show that a penalty function of the shape h 2 p leads to a quasi-optimal convergence of the scheme. Some numerical experiments confirm the expected rates of convergence and the effect of the penalty function. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 08981221
- Volume :
- 80
- Issue :
- 12
- Database :
- Academic Search Index
- Journal :
- Computers & Mathematics with Applications
- Publication Type :
- Academic Journal
- Accession number :
- 147460031
- Full Text :
- https://doi.org/10.1016/j.camwa.2020.10.013