Back to Search
Start Over
Robust convergence result of discontinuous Galerkin stabilization method for two-dimensional reaction–diffusion equation with discontinuous source term.
- Source :
-
International Journal of Computer Mathematics . Mar2024, Vol. 101 Issue 3, p255-280. 26p. - Publication Year :
- 2024
-
Abstract
- A reaction–diffusion problem with discontinuous source term and Dirichlet's boundary conditions on the unit square is considered in this paper. The proposed problem has been discretized using a combination of standard Galerkin finite element method (FEM) and non-symmetric discontinuous Galerkin finite element method with an interior penalty (NIPG) with bilinear elements. Layer adapted mesh of Shishkin type has been utilized to discretize the domain. Standard Galerkin FEM is applied on the layer part of the domain where the domain is dense enough and NIPG is applied to the outside layer part. By means of special choice of discontinuity-penalization parameters, the scheme is proved to be uniformly convergent of order $ \mathcal {O}(\varepsilon ^{1/4}N^{-1} + N^{-1} \ln N) $ O (ε 1 / 4 N − 1 + N − 1 ln N). Numerical tests are carried out in support of theoretical findings. [ABSTRACT FROM AUTHOR]
- Subjects :
- *GALERKIN methods
*FINITE element method
*DISCONTINUOUS functions
Subjects
Details
- Language :
- English
- ISSN :
- 00207160
- Volume :
- 101
- Issue :
- 3
- Database :
- Academic Search Index
- Journal :
- International Journal of Computer Mathematics
- Publication Type :
- Academic Journal
- Accession number :
- 176147007
- Full Text :
- https://doi.org/10.1080/00207160.2024.2325676