## ERROR ESTIMATES FOR NONLINEAR CONVECTIVE PROBLEMS IN THE FINITE ELEMENT METHOD

- ID: 2575, RIV: 10190669
- ISSN: not specified, ISBN: 978-80-85823-62-2
- source: PROGRAMS AND ALGORITHMS OF NUMERICAL MATHEMATICS 16
- keywords: Discontinuous Galerkin; error estimates; nonlinear convective problems
- authors: Václav Kučera
- authors from KNM: Kučera Václav

### Abstract

We describe the basic ideas needed to obtain apriori error estimates for a nonlinear convection diffusion equation discretized by higher order conforming finite elements. For simplicity of presentation, we derive the key estimates under simplified assumptions, e.g. Dirichlet-only boundary conditions. The resulting error estimate is obtained using continuous mathematical induction for the space semi-discrete scheme.