A parallel hp-adaptive discontinuous Galerkin method for hyperbolic conservation laws
Applied Numerical Mathematics - Special issue on adaptive mesh refinement methods for CFD applications
Runge–Kutta Discontinuous Galerkin Methods for Convection-Dominated Problems
Journal of Scientific Computing
hp-Adaptive Discontinuous Galerkin Finite Element Methods for First-Order Hyperbolic Problems
SIAM Journal on Scientific Computing
Nodal high-order methods on unstructured grids
Journal of Computational Physics
Thehp-local discontinuous Galerkin method for low-frequency time-harmonic Maxwell equations
Mathematics of Computation
Shock detection and limiting with discontinuous Galerkin methods for hyperbolic conservation laws
Applied Numerical Mathematics - Special issue: Workshop on innovative time integrators for PDEs
Journal of Computational Physics
Arbitrary-level hanging nodes and automatic adaptivity in the hp-FEM
Mathematics and Computers in Simulation
Nodal Discontinuous Galerkin Methods: Algorithms, Analysis, and Applications
Nodal Discontinuous Galerkin Methods: Algorithms, Analysis, and Applications
A hybrid Finite Integration-Finite Volume Scheme
Journal of Computational Physics
An hp-adaptive strategy based on continuous Sobolev embeddings
Journal of Computational and Applied Mathematics
Journal of Computational Physics
hp-FEM electromechanical transduction model of ionic polymer-metal composites
Journal of Computational and Applied Mathematics
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A framework for performing dynamic mesh adaptation with the discontinuous Galerkin method (DGM) is presented. Adaptations include modifications of the local mesh step size (h-adaptation) and the local degree of the approximating polynomials (p-adaptation) as well as their combination. The computation of the approximation within locally adapted elements is based on projections between finite element spaces (FES), which are shown to preserve an upper limit of the electromagnetic energy. The formulation supports high level hanging nodes and applies precomputation of surface integrals for increasing computational efficiency. Error and smoothness estimates based on interface jumps are presented and applied to the fully hp-adaptive simulation of two examples in one-dimensional space. A full wave simulation of electromagnetic scattering from a radar reflector demonstrates the applicability to large scale problems in three-dimensional space.