The Local Discontinuous Galerkin Method for Time-Dependent Convection-Diffusion Systems
SIAM Journal on Numerical Analysis
Finite Element Method for Elliptic Problems
Finite Element Method for Elliptic Problems
An A Priori Error Analysis of the Local Discontinuous Galerkin Method for Elliptic Problems
SIAM Journal on Numerical Analysis
Local Discontinuous Galerkin Methods for the Stokes System
SIAM Journal on Numerical Analysis
Mixed hp-DGFEM for Incompressible Flows
SIAM Journal on Numerical Analysis
An hp-Analysis of the Local Discontinuous Galerkin Method for Diffusion Problems
Journal of Scientific Computing
SIAM Journal on Scientific Computing
Journal of Scientific Computing
A mixed local discontinuous Galerkin method for a class of nonlinear problems in fluid mechanics
Journal of Computational Physics
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In this paper we analyze the main features of the local discontinuous Galerkin method applied to nonlinear boundary value problems in the plane. We consider a class of nonlinear elliptic problems arising in heat conduction and fluid mechanics. The approach, which has been originally applied to several linear boundary value problems, is based on the introduction of additional unknowns given by the flux and the gradient of the temperature (velocity) for diffusion problems (fluid mechanics), and considers convex and nonconvex bounded domains with polygonal boundaries. Our present analysis unifies and simplifies the derivation of the results given in previous works. Several numerical examples are presented, which validate our theoretical results.