Parallel, adaptive finite element methods for conservation laws
Proceedings of the third ARO workshop on Adaptive methods for partial differential equations
Monotone multigrid methods for elliptic variational inequalities I
Numerische Mathematik
Parallel adaptive hp-refinement techniques for conservation laws
Applied Numerical Mathematics - Special issue on adaptive mesh refinement methods for CFD applications
Journal of Computational Physics
Parallel structures and dynamic load balancing for adaptive finite element computation
Proceedings of international centre for mathematical sciences on Grid adaptation in computational PDES : theory and applications: theory and applications
The Local Discontinuous Galerkin Method for Time-Dependent Convection-Diffusion Systems
SIAM Journal on Numerical Analysis
A Discontinuous Galerkin Finite Element Method for Hamilton--Jacobi Equations
SIAM Journal on Scientific Computing
Discretized obstacle problems with penalties on nested grids
Applied Numerical Mathematics
Analysis of the discontinuous Galerkin method for Hamilton—Jacobi equations
Proceedings of the fourth international conference on Spectral and high order methods (ICOSAHOM 1998)
hp-Adaptive Discontinuous Galerkin Finite Element Methods for First-Order Hyperbolic Problems
SIAM Journal on Scientific Computing
Discontinuous hp-Finite Element Methods for Advection-Diffusion-Reaction Problems
SIAM Journal on Numerical Analysis
Unified Analysis of Discontinuous Galerkin Methods for Elliptic Problems
SIAM Journal on Numerical Analysis
Stabilized hp-Finite Element Methods for First-Order Hyperbolic 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
Applied Numerical Mathematics
Discrete-Ordinate Discontinuous Galerkin Methods for Solving the Radiative Transfer Equation
SIAM Journal on Scientific Computing
Discontinuous Galerkin Methods: Theory, Computation and Applications
Discontinuous Galerkin Methods: Theory, Computation and Applications
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We study discontinuous Galerkin methods for solving elliptic variational inequalities of both the first and second kinds. Analysis of numerous discontinuous Galerkin schemes for elliptic boundary value problems is extended to the variational inequalities. We establish a priori error estimates for the discontinuous Galerkin methods, which reach optimal order for linear elements. Results from some numerical examples are reported.