Estimation of modeling error in computational mechanics
Journal of Computational Physics
Adaptive discontinuous Galerkin finite element methods for the compressible Euler equations
Journal of Computational Physics
Anisotropic grid adaptation for functional outputs: application to two-dimensional viscous flows
Journal of Computational Physics
Mass preserving finite element implementations of the level set method
Applied Numerical Mathematics - Numerical methods for viscosity solutions and applications
Discontinuous Galerkin methods on hp-anisotropic meshes I: a priori error analysis
International Journal of Computing Science and Mathematics
Applied Numerical Mathematics
Adjoint-based h-p adaptive discontinuous Galerkin methods for the 2D compressible Euler equations
Journal of Computational Physics
Finite volume multischeme for hyperbolic conservation laws
FANDB'09 Proceedings of the 2nd WSEAS international conference on Finite differences, finite elements, finite volumes, boundary elements
Error analysis for optimal control problem governed by convection diffusion equations: DG method
Journal of Computational and Applied Mathematics
Discontinuous Galerkin Methods for Solving Elliptic Variational Inequalities
SIAM Journal on Numerical Analysis
SIAM Journal on Scientific Computing
SIAM Journal on Control and Optimization
On the discontinuous galerkin method for friedrichs systems in graph spaces
LSSC'05 Proceedings of the 5th international conference on Large-Scale Scientific Computing
Journal of Computational and Applied Mathematics
Journal of Computational Physics
Hi-index | 0.03 |
We consider the {a posteriori} error analysis of hp-discontinuous Galerkin finite element approximations to first-order hyperbolic problems. In particular, we discuss the question of error estimation for linear functionals, such as the outflow flux and the local average of the solution. Based on our {a posteriori} error bound we design and implement the corresponding adaptive algorithm to ensure reliable and efficient control of the error in the prescribed functional to within a given tolerance. This involves exploiting both local polynomial-degree variation and local mesh subdivision. The theoretical results are illustrated by a series of numerical experiments.