A discontinuous hp finite element method for diffusion problems
Journal of Computational Physics
The Local Discontinuous Galerkin Method for Time-Dependent Convection-Diffusion Systems
SIAM Journal on Numerical Analysis
An optimal domain decomposition preconditioner for low-frequency time-harmonic Maxwell equations
Mathematics of Computation
A singular field method for the solution of Maxwell's equations in polyhedral domains
SIAM Journal on Applied Mathematics
On the Coupling of Local Discontinuous Galerkin and Conforming Finite Element Methods
Journal of Scientific Computing
Runge–Kutta Discontinuous Galerkin Methods for Convection-Dominated Problems
Journal of Scientific Computing
Finite Element Method for Elliptic Problems
Finite Element Method for Elliptic Problems
Discontinuous hp-Finite Element Methods for Advection-Diffusion-Reaction Problems
SIAM Journal on Numerical Analysis
Superconvergence of the Local Discontinuous Galerkin Method for Elliptic Problems on Cartesian Grids
SIAM Journal on Numerical Analysis
Unified Analysis of Discontinuous Galerkin Methods for Elliptic Problems
SIAM Journal on Numerical Analysis
SIAM Journal on Numerical Analysis
An A Priori Error Analysis of the Local Discontinuous Galerkin Method for Elliptic Problems
SIAM Journal on Numerical Analysis
An hp-Analysis of the Local Discontinuous Galerkin Method for Diffusion Problems
Journal of Scientific Computing
Mixed finite element approximation of incompressible MHD problems based on weighted regularization
Applied Numerical Mathematics
Mixed Discontinuous Galerkin Approximation of the Maxwell Operator: Non-Stabilized Formulation
Journal of Scientific Computing
A mixed local discontinuous Galerkin method for a class of nonlinear problems in fluid mechanics
Journal of Computational Physics
Mixed discontinuous Galerkin approximation of the Maxwell operator: non-stabilized formulation
Journal of Scientific Computing
An interior penalty Galerkin method for the MHD equations in heterogeneous domains
Journal of Computational Physics
Journal of Computational and Applied Mathematics
Journal of Scientific Computing
Quasi-Optimal Convergence Rate of an Adaptive Discontinuous Galerkin Method
SIAM Journal on Numerical Analysis
Numerical analysis of a PML model for time-dependent Maxwell's equations
Journal of Computational and Applied Mathematics
Hybridizable discontinuous Galerkin methods for the time-harmonic Maxwell's equations
Journal of Computational Physics
Journal of Computational and Applied Mathematics
SIAM Journal on Scientific Computing
Hi-index | 0.02 |
The local discontinuous Galerkin method for the numerical approximation of the time-harmonic Maxwell equations in a low-frequency regime is introduced and analyzed. Topologically nontrivial domains and heterogeneous media are considered, containing both conducting and insulating materials. The presented method involves discontinuous Galerkin discretizations of the curl-curl and grad-div operators, derived by introducing suitable auxiliary variables and so-called numerical fluxes. An hp-analysis is carried out and error estimates that are optimal in the meshsize h and slightly suboptimal in the approximation degree p are obtained.