Abstract
A Petrov-Galerkin finite element method is constructed for a singularly perturbed elliptic problem in two space dimensions. The solution contains a regular boundary layer and two characteristic boundary layers. Exponential splines are used as test functions in one coordinate direction and are combined with bilinear trial functions defined on a Shishkin mesh. The resulting numerical method is shown to be a stable parameter-uniform numerical method that achieves a higher order of convergence compared to upwinding on the same mesh.
Original language | English |
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Pages (from-to) | 85-101 |
Number of pages | 17 |
Journal | Applied Numerical Mathematics |
Volume | 201 |
DOIs | |
Publication status | Published - Jul 2024 |
Keywords
- Convection-diffusion
- Higher order
- Petrov-Galerkin
- Shishkin mesh