Stability and convergence of a finite element method for a semilinear elliptical problem with small viscosity

Abstract In this paper, we propose and analyze a new finite element method for a semilinear elliptical problem with small viscosity. Firstly, we prove the existence and uniqueness of solution for its variational problem. Then, we obtain the stability and convergence of the corresponding finite element Galerkin approximation. Furthermore, we derive the optimal error estimates in the L 2 and H 1 norms for the finite element approximations respectively. Finally, several numerical experiments are provided to confirm the above theoretical results.

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