Stabilizer-free weak Galerkin methods for monotone quasilinear elliptic PDEs

Abstract

In this paper, we study the stabilizer-free weak Galerkin methods on polytopal meshes for a class of second order elliptic boundary value problems of divergence form and with gradient nonlinearity in the principal coefficient. With certain assumptions on the nonlinear coefficient, we show that the discrete problem has a unique solution. This is achieved by showing that the associated operator satisfies certain continuity and monotonicity properties. With the help of these properties, we derive optimal error estimates in the energy norm. We present several numerical examples to verify the error estimates.

Keywords

• Uniqueness
• Monotone PDEs
• Quasilinear equations
• Weak Galerkin methods
• Stabilizer-free