Abstract
We consider a convection-diffusion problem with Dirichlet boundary conditions posed on a unit square. The problem is discretized using a combination of the standard Galerkin FEM and an h-version of the non-symmetric discontinuous Galerkin FEM with interior penalties on a layer-adapted mesh with linear/bilinear elements. With specially chosen penalty parameters for edges from the coarse part of the mesh, we prove uniform convergence (in the perturbation parameter) in an associated norm. In the same norm we also establish a supercloseness result. Numerical tests support our theoretical estimates.
Original language | English (US) |
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Pages (from-to) | 1560-1576 |
Number of pages | 17 |
Journal | Numerical Methods for Partial Differential Equations |
Volume | 23 |
Issue number | 6 |
DOIs | |
State | Published - Nov 2007 |
Externally published | Yes |
Keywords
- Convection-diffusion problem
- Finite element method
- Interior penalty
- Layer-adapted mesh
- Singular perturbation
- Superconvergence