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THE (p, p - 1)-HDG METHOD FOR THE HELMHOLTZ EQUATION WITH LARGE WAVE NUMBER.
- Source :
- SIAM Journal on Numerical Analysis; 2024, Vol. 62 Issue 3, p1394-1419, 26p
- Publication Year :
- 2024
-
Abstract
- In this paper, we analyze a hybridizable discontinuous Galerkin method for the Helmholtz equation with large wave number, which uses piecewise polynomials of degree of p ≥ 1 to approximate the potential u and its traces and piecewise polynomials of degree of p - 1 for the flux q. It is proved that ... and ... hold under the conditions that k(kh)<superscript>2p</superscript> is sufficiently small and that the penalty parameter ..., where h is the mesh size. Numerical experiments are proposed to verify our theoretical findings and to show that the pollution error may be greatly reduced by tuning the penalty parameter. [ABSTRACT FROM AUTHOR]
- Subjects :
- WAVENUMBER
WAVE equation
GALERKIN methods
HELMHOLTZ equation
POLYNOMIALS
Subjects
Details
- Language :
- English
- ISSN :
- 00361429
- Volume :
- 62
- Issue :
- 3
- Database :
- Complementary Index
- Journal :
- SIAM Journal on Numerical Analysis
- Publication Type :
- Academic Journal
- Accession number :
- 178433217
- Full Text :
- https://doi.org/10.1137/23M1562639