Abstract
Uniform discrete Sobolev space estimates are proven for a class of finite-difference schemes for singularly-perturbed hyperbolic-parabolic systems. The estimates obtained improve previous results even when the PDEs do not involve singular perturbations. These estimates are used in a companion paper to prove the convergence of solutions as the discretization parameter and/or the singular perturbation parameter tends to zero.
| Original language | English |
|---|---|
| Pages (from-to) | 727-757 |
| Number of pages | 31 |
| Journal | ESAIM: Mathematical Modelling and Numerical Analysis |
| Volume | 51 |
| Issue number | 2 |
| DOIs | |
| State | Published - 1 Mar 2017 |
Keywords
- Discrete Sobolev spaces
- Finite-difference methods
- Fully-discrete sharp Gårding inequality
- Singular limits
- Uniform estimates
All Science Journal Classification (ASJC) codes
- Analysis
- Numerical Analysis
- Modelling and Simulation
- Computational Mathematics
- Applied Mathematics
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