A Local Discontinuous Galerkin Method for Nonlinear Diffusion Problems with Mixed Boundary Conditions

In this paper we present and analyze a local discontinuous Galerkin method for a class of nonlinear diffusion problems in polygonal regions of $\R^2$. Our analysis follows known approaches previously applied to linear problems and considers convex and nonconvex domains. We provide solvability and stability of the discrete scheme for several polynomial approximations, and we derive a priori error estimates in the energy and L2 norms. Numerical experiments illustrating these results are also provided.

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