An analysis of the discontinuous Galerkin method for a scalar hyperbolic equation
Mathematics of Computation
A discontinuous hp finite element method for diffusion problems
Journal of Computational Physics
Discontinuous hp-Finite Element Methods for Advection-Diffusion-Reaction Problems
SIAM Journal on Numerical Analysis
SIAM Journal on Numerical Analysis
Unified Analysis of Discontinuous Galerkin Methods for Elliptic Problems
SIAM Journal on Numerical Analysis
An A Priori Error Analysis of the Local Discontinuous Galerkin Method for Elliptic Problems
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 Numerical Analysis
Local discontinuous Galerkin methods for nonlinear dispersive equations
Journal of Computational Physics
SIAM Journal on Numerical Analysis
SIAM Journal on Scientific Computing
Journal of Scientific Computing
An A Posteriori Error Estimate for the Local Discontinuous Galerkin Method
Journal of Scientific Computing
A mixed local discontinuous Galerkin method for a class of nonlinear problems in fluid mechanics
Journal of Computational Physics
Convergence of Adaptive Discontinuous Galerkin Approximations of Second-Order Elliptic Problems
SIAM Journal on Numerical Analysis
A posteriori error estimators for locally conservative methods of nonlinear elliptic problems
Applied Numerical Mathematics
Discontinuous Galerkin Methods for Quasi-Linear Elliptic Problems of Nonmonotone Type
SIAM Journal on Numerical Analysis
SIAM Journal on Numerical Analysis
Discontinuous Galerkin Methods For Solving Elliptic And parabolic Equations: Theory and Implementation
Journal of Computational and Applied Mathematics
Discontinuous Galerkin Methods for Second-Order Elliptic PDE with Low-Regularity Solutions
Journal of Scientific Computing
Two-Grid Discontinuous Galerkin Method for Quasi-Linear Elliptic Problems
Journal of Scientific Computing
Discontinuous Galerkin Methods: Theory, Computation and Applications
Discontinuous Galerkin Methods: Theory, Computation and Applications
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In this paper, we propose and study the residual-based a posteriori error estimates of h-version of symmetric interior penalty discontinuous Galerkin method for solving a class of second order quasi-linear elliptic problems which are of nonmonotone type. Computable upper and lower bounds on the error measured in terms of a natural mesh-dependent energy norm and the broken H 1-seminorm, respectively, are derived. Numerical experiments are also provided to illustrate the performance of the proposed estimators.