A stabilized finite element method for advection-diffusion equations on surfaces. (English) Zbl 1293.65159
This paper presents a volume mesh finite element method (FEM) for linear advection-diffusion equations on two-dimensional surfaces embedded in \(\mathbb{R}^3\). The emphasis is put on the convection dominated regime and stabilization of the method by a surface variant of the streamline upwind Petrov-Galerkin (SUPG) technique. The main contribution of the paper is the presented error analysis. A nearly optimal error estimate in a mesh dependent norm is proved. The analysis is provided for the stationary problem only, but the numerical experiments show the accuracy of the method for both the evolutionary and the stationary case.
Reviewer: Tomas Vejchodsky (Praha)
MSC:
65N30 | Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs |
65N15 | Error bounds for boundary value problems involving PDEs |
35J25 | Boundary value problems for second-order elliptic equations |
35K20 | Initial-boundary value problems for second-order parabolic equations |
65M60 | Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs |
65N12 | Stability and convergence of numerical methods for boundary value problems involving PDEs |