Runge–Kutta Discontinuous Galerkin Methods for Convection-Dominated Problems
Journal of Scientific Computing
An adaptive higher order method for solving the radiation transport equation on unstructured grids
Journal of Computational Physics
Aspects of discontinuous Galerkin methods for hyperbolic conservation laws
Finite Elements in Analysis and Design - Robert J. Melosh medal competition
hp-Discontinuous Galerkin Finite Element Methods with Least-Squares Stabilization
Journal of Scientific Computing
A Fully Automatic hp-Adaptivity
Journal of Scientific Computing
Finite element analysis of convection dominated reaction-diffusion problems
Applied Numerical Mathematics
Discontinuous Galerkin methods on hp-anisotropic meshes I: a priori error analysis
International Journal of Computing Science and Mathematics
Journal of Computational Physics
SIAM Journal on Numerical Analysis
Discontinuous Galerkin Methods for Solving Elliptic Variational Inequalities
SIAM Journal on Numerical Analysis
Analysis of an Interface Stabilized Finite Element Method: The Advection-Diffusion-Reaction Equation
SIAM Journal on Numerical Analysis
On the discontinuous galerkin method for friedrichs systems in graph spaces
LSSC'05 Proceedings of the 5th international conference on Large-Scale Scientific Computing
A class of discontinuous Petrov-Galerkin methods. Part III: Adaptivity
Applied Numerical Mathematics
High order splitting schemes with complex timesteps and their application in mathematical finance
Journal of Computational and Applied Mathematics
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We analyze the hp-version of the streamline-diffusion finite element method (SDFEM) and of the discontinuous Galerkin finite element method (DGFEM) for first-order linear hyperbolic problems. For both methods, we derive new error estimates on general finite element meshes which are sharp in the mesh-width h and in the spectral order p of the method, assuming that the stabilization parameter is O(h/p). For piecewise analytic solutions, exponential convergence is established on quadrilateral meshes. For the DGFEM we admit very general irregular meshes and for the SDFEM we allow meshes which contain hanging nodes. Numerical experiments confirm the theoretical results.