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

Authors:
Rommel Bustinza;Gabriel N. Gatica
Affiliations:
-;-
Venue:
SIAM Journal on Scientific Computing
Year:
2005

Citing 0
Cited 7

An A Posteriori Error Estimate for the Local Discontinuous Galerkin Method Applied to Linear and Nonlinear Diffusion Problems

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A mixed local discontinuous Galerkin method for a class of nonlinear problems in fluid mechanics

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An a posteriori error estimate for the local discontinuous Galerkin method applied to linear and nonlinear diffusion problems

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A unified analysis of the local discontinuous Galerkin method for a class of nonlinear problems

Applied Numerical Mathematics - Selected papers from the first Chilean workshop on numerical analysis of partial differential equations (WONAPDE 2004)
A posteriori error estimators for locally conservative methods of nonlinear elliptic problems

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Superconvergent Discontinuous Galerkin Methods for Linear Non-selfadjoint and Indefinite Elliptic Problems

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A Posteriori Error Estimates of Discontinuous Galerkin Method for Nonmonotone Quasi-linear Elliptic Problems

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Abstract

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.