Selecting the Numerical Flux in Discontinuous Galerkin Methods for Diffusion Problems
Journal of Scientific Computing
Analysis of a Discontinuous Finite Element Method for the Coupled Stokes and Darcy Problems
Journal of Scientific Computing
Journal of Scientific Computing
Discontinuous Galerkin methods for coupled flow and reactive transport problems
Applied Numerical Mathematics - Adaptive methods for partial differential equations and large-scale computation
Selecting the numerical flux in discontinuous Galerkin methods for diffusion problems
Journal of Scientific Computing
Analysis of a discontinuous finite element method for the coupled stokes and Darcy problems
Journal of Scientific Computing
Journal of Scientific Computing
Journal of Computational Physics
Analysis of Discontinuous Galerkin Methods for Multicomponent Reactive Transport Problems
Computers & Mathematics with Applications
Journal of Computational and Applied Mathematics
Estimation of penalty parameters for symmetric interior penalty Galerkin methods
Journal of Computational and Applied Mathematics
Finite Elements in Analysis and Design
Journal of Computational and Applied Mathematics
Multiscale Discontinuous Galerkin Methods for Modeling Flow and Transport in Porous Media
ICCS '07 Proceedings of the 7th international conference on Computational Science, Part I: ICCS 2007
Mixed Discontinuous Galerkin Finite Element Method for the Biharmonic Equation
Journal of Scientific Computing
Discontinuous Galerkin methods for the chemotaxis and haptotaxis models
Journal of Computational and Applied Mathematics
Analysis of hp discontinuous Galerkin methods for incompressible two-phase flow
Journal of Computational and Applied Mathematics
Numerical solution of a one-dimensional inverse problem by the discontinuous Galerkin method
Mathematics and Computers in Simulation
Journal of Computational and Applied Mathematics
Uniformly Convergent Iterative Methods for Discontinuous Galerkin Discretizations
Journal of Scientific Computing
Journal of Scientific Computing
Journal of Scientific Computing
Journal of Scientific Computing
Primal Discontinuous Galerkin Methods for Time-Dependent Coupled Surface and Subsurface Flow
Journal of Scientific Computing
Discontinuous Galerkin methods for coupled flow and reactive transport problems
Applied Numerical Mathematics - Adaptive methods for partial differential equations and large-scale computation
On the Suboptimality of the p-Version Interior Penalty Discontinuous Galerkin Method
Journal of Scientific Computing
Journal of Computational Physics
A strongly conservative finite element method for the coupling of Stokes and Darcy flow
Journal of Computational Physics
Some nonstandard error analysis of discontinuous Galerkin methods for elliptic problems
Calcolo: a quarterly on numerical analysis and theory of computation
An hp-local Discontinuous Galerkin Method for Parabolic Integro-Differential Equations
Journal of Scientific Computing
Discontinuous Galerkin Methods for Second-Order Elliptic PDE with Low-Regularity Solutions
Journal of Scientific Computing
Error analysis for optimal control problem governed by convection diffusion equations: DG method
Journal of Computational and Applied Mathematics
Journal of Scientific Computing
Bubble stabilized discontinuous Galerkin methods on conforming and non-conforming meshes
Calcolo: a quarterly on numerical analysis and theory of computation
Two-Grid Discontinuous Galerkin Method for Quasi-Linear Elliptic Problems
Journal of Scientific Computing
A discontinuous Galerkin method for the Vlasov-Poisson system
Journal of Computational Physics
A discontinuous finite element method for image denoising
ICIAR'06 Proceedings of the Third international conference on Image Analysis and Recognition - Volume Part I
Higher order weakly over-penalized symmetric interior penalty methods
Journal of Computational and Applied Mathematics
A discontinuous Galerkin method for gravity-driven viscous fingering instabilities in porous media
Journal of Computational Physics
A weak Galerkin finite element method for second-order elliptic problems
Journal of Computational and Applied Mathematics
A New Nonsymmetric Discontinuous Galerkin Method for Time Dependent Convection Diffusion Equations
Journal of Scientific Computing
Journal of Scientific Computing
Parallel mesh adaptive techniques illustrated with complex compressible flow simulations
Modelling and Simulation in Engineering
A posteriori error estimates of hp-adaptive IPDG-FEM for elliptic obstacle problems
Applied Numerical Mathematics
Computers & Mathematics with Applications
hp-adaptive IPDG/TDG-FEM for parabolic obstacle problems
Computers & Mathematics with Applications
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We analyze three discontinuous Galerkin approximations for solving elliptic problems in two or three dimensions. In each one, the basic bilinear form is nonsymmetric: the first one has a penalty term on edges, the second has one constraint per edge, and the third is totally unconstrained. For each of them we prove hp error estimates in the H1 norm, optimal with respect to h, the mesh size, and nearly optimal with respect to p, the degree of polynomial approximation. We establish these results for general elements in two and three dimensions. For the unconstrained method, we establish a new approximation result valid on simplicial elements. L2 estimates are also derived for the three methods.