Mixed Discontinuous Galerkin Approximation of the Maxwell Operator: Non-Stabilized Formulation
Journal of Scientific Computing
Journal of Scientific Computing
Mixed discontinuous Galerkin approximation of the Maxwell operator: non-stabilized formulation
Journal of Scientific Computing
Journal of Scientific Computing
Viscous stabilization of discontinuous Galerkin solutions of hyperbolic conservation laws
Applied Numerical Mathematics - The third international conference on the numerical solutions of volterra and delay equations, May 2004, Tempe, AZ
Journal of Computational Physics
Journal of Computational and Applied Mathematics
Interior penalty discontinuous Galerkin method for Maxwell's equations: Energy norm error estimates
Journal of Computational and Applied Mathematics
Journal of Computational and Applied Mathematics
Error analysis of mixed finite element methods for wave propagation in double negative metamaterials
Journal of Computational and Applied Mathematics
Journal of Scientific Computing
A Mixed DG Method for Linearized Incompressible Magnetohydrodynamics
Journal of Scientific Computing
Viscous stabilization of discontinuous Galerkin solutions of hyperbolic conservation laws
Applied Numerical Mathematics
Explicit local time-stepping methods for Maxwell's equations
Journal of Computational and Applied Mathematics
Approximation of the thermally coupled MHD problem using a stabilized finite element method
Journal of Computational Physics
Certified Reduced Basis Methods and Output Bounds for the Harmonic Maxwell's Equations
SIAM Journal on Scientific Computing
Solving Maxwell's equations in singular domains with a Nitsche type method
Journal of Computational Physics
A Nodal-based Finite Element Approximation of the Maxwell Problem Suitable for Singular Solutions
SIAM Journal on Numerical Analysis
Journal of Computational Physics
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We introduce and analyze a discontinuous Galerkin discretization of the Maxwell operator in mixed form. Here, all the unknowns of the underlying system of partial differential equations are approximated by discontinuous finite element spaces of the same order. For piecewise constant coefficients, the method is shown to be stable and optimally convergent with respect to the mesh size. Numerical experiments highlighting the performance of the proposed method for problems with both smooth and singular analytical solutions are presented.