Stabilized finite element methods with shock-capturing for nonlinear convection-diffusion-reaction models. (English) Zbl 1216.65152
Kreiss, Gunilla (ed.) et al., Numerical mathematics and advanced applications 2009. Proceedings of ENUMATH 2009, the 8th European conference on numerical mathematics and advanced applications, Uppsala, Sweden, June 29–July 3, 2009. Berlin: Springer (ISBN 978-3-642-11794-7/hbk; 978-3-642-11795-4/ebook). 125-133 (2010).
Summary: Stabilized higher-order finite element approximations of convection-diffusion-reactions models with nonlinear reaction mechanisms are studied. Streamline upwind Petrov-Galerkin (SUPG) stabilization together with anisotropic shock-capturing as an additional stabilization in crosswind-direction is used. The parameter design of the scheme is described precisely and error estimates are provided. Theoretical results are illustrated by numerical computations. The work extends former investigations for linear problems to more realistic nonlinear models.
For the entire collection see [Zbl 1201.65003].
For the entire collection see [Zbl 1201.65003].
MSC:
| 65N30 | Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs |
| 35J65 | Nonlinear boundary value problems for linear elliptic equations |
| 65N12 | Stability and convergence of numerical methods for boundary value problems involving PDEs |
| 65N15 | Error bounds for boundary value problems involving PDEs |
