hp-Discontinuous Galerkin Finite Element Methods with Least-Squares Stabilization
Journal of Scientific Computing
Thehp-local discontinuous Galerkin method for low-frequency time-harmonic Maxwell equations
Mathematics of Computation
Multilevel a posteriori error analysis for reaction—convection—diffusion problems
Applied Numerical Mathematics
Dispersive and dissipative behaviour of high order discontinuous Galerkin finite element methods
Journal of Computational Physics
Journal of Scientific Computing
Journal of Scientific Computing
Algebraic Fractional-Step Schemes for Time-Dependent Incompressible Navier---Stokes Equations
Journal of Scientific Computing
Space-time discontinuous Galerkin method for advection-diffusion problems on time-dependent domains
Applied Numerical Mathematics
Fully implicit discontinuous finite element methods for two-phase flow
Applied Numerical Mathematics
Journal of Computational and Applied Mathematics
Journal of Computational Physics
Estimation of penalty parameters for symmetric interior penalty Galerkin methods
Journal of Computational and Applied Mathematics
Finite Elements in Analysis and Design
Minimal Stabilization for Discontinuous Galerkin Finite Element Methods for Hyperbolic Problems
Journal of Scientific Computing
Journal of Computational and Applied Mathematics
Discontinuous Galerkin methods on hp-anisotropic meshes I: a priori error analysis
International Journal of Computing Science and Mathematics
Journal of Computational and Applied Mathematics
Journal of Computational and Applied Mathematics
Efficient preconditioning for the discontinuous Galerkin finite element method by low-order elements
Applied Numerical Mathematics
Applied Numerical Mathematics
Journal of Computational and Applied Mathematics
Stability and error analysis of mixed finite-volume methods for advection dominated problems
Computers & Mathematics with Applications
On the Suboptimality of the p-Version Interior Penalty Discontinuous Galerkin Method
Journal of Scientific Computing
A Class of Domain Decomposition Preconditioners for hp-Discontinuous Galerkin Finite Element Methods
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
Optimal Convergence of the Original DG Method on Special Meshes for Variable Transport Velocity
SIAM Journal on Numerical Analysis
Discontinuous Galerkin Methods for Solving Elliptic Variational Inequalities
SIAM Journal on Numerical Analysis
Quasi-Optimal Convergence Rate of an Adaptive Discontinuous Galerkin Method
SIAM Journal on Numerical Analysis
A Hybrid Discontinuous Galerkin Method for Elliptic Problems
SIAM Journal on Numerical Analysis
Two-Grid Discontinuous Galerkin Method for Quasi-Linear Elliptic Problems
Journal of Scientific Computing
Benchmark results for testing adaptive finite element eigenvalue procedures
Applied Numerical Mathematics
A Posteriori Error Control for Discontinuous Galerkin Methods for Parabolic Problems
SIAM Journal on Numerical Analysis
Journal of Computational Physics
A class of discontinuous Petrov-Galerkin methods. Part III: Adaptivity
Applied Numerical Mathematics
Locking-Free Optimal Discontinuous Galerkin Methods for a Naghdi-Type Arch Model
Journal of Scientific Computing
Journal of Computational and Applied Mathematics
SIAM Journal on Scientific Computing
Journal of Scientific Computing
Journal of Scientific Computing
Computers & Mathematics with Applications
On the stability of the boundary trace of the polynomial L2-projection on triangles and tetrahedra
Computers & Mathematics with Applications
Computational Optimization and Applications
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We consider the hp-version of the discontinuous Galerkin finite element method (DGFEM) for second-order partial differential equations with nonnegative characteristic form. This class of equations includes second-order elliptic and parabolic equations, advection-reaction equations, as well as problems of mixed hyperbolic-elliptic-parabolic type. Our main concern is the error analysis of the method in the absence of streamline-diffusion stabilization. In the hyperbolic case, an hp-optimal error bound is derived; here, we consider only advection-reaction problems which satisfy a certain (standard) positivity condition. In the self-adjoint elliptic case, an error bound that is h-optimal and p-suboptimal by $\frac{1}{2}$ a power of p is obtained. These estimates are then combined to deduce an error bound in the general case. For elementwise analytic solutions the method exhibits exponential rates of convergence under p-refinement. The theoretical results are illustrated by numerical experiments.