Stabilized finite element methods for singularly perturbed parabolic problems
The authors consider two stabilized numerical schemes for solving Dirichlet-type initial-boundary value problems of the parabolic equation \((\partial_t + L_\varepsilon) u : = \partial_t u - \varepsilon \Delta u + b \cdot \nabla u + cu = f\), modelling convection-reaction-diffusion. Weighted least squares forms of the underlying equation are added to the basic Galerkin finite element semidiscretization in order to accomodate the method to (possibly locally varying) convective, reactive or diffusive terms. Time integration is performed with standard stable one-step methods. Stability and error estimates are derived on unstructured grids and the design of the numerical damping parameters are considered. Numerical results are given for typical model problems, including ``translating cone''.
Galerkin finite element semidiscretization
scientific article; zbMATH DE number 817335
scientific article