This paper analyzes the limits of applicability of the time domain surface impedance concept. Numerical results obtained by the boundary element formulation employing time domain surface impedance boundary conditions (SIBCs) of different orders of approximation are compared with experimental data and numerical results obtained using the finite element method. An analytical formula for evaluatio...

Discontinuous Galerkin methods are developed for solving the Vlasov–Maxwell system, methods that are designed to be systematically as accurate as one wants with provable conservation of mass and possibly total energy. Such properties in general are hard to achieve within other numerical method frameworks for simulating the Vlasov–Maxwell system. The proposed scheme employs discontinuous Galerki...

Weighted essentially non-oscillatory (WENO) methods can simultaneously provide the high order of accuracy, high bandwidth-resolving efficiency, and shock-capturing capability required for the detailed simulation of compressible turbulence. However, rigorous analysis of the actual versus theoretical error properties of these non-linear numerical methods is difficult. We use a bandwidth-optimized...

A postprocessing technique based on negative order norm estimates for the discontinuous Galerkin methods was previously introduced by Cockburn, Luskin, Shu, and Süli [Proceedings of the International Symposium on Discontinuous Galerkin Methods, Springer, New York, pp. 291– 300; Math. Comput., 72 (2003), pp. 577–606]. The postprocessor allows improvement in accuracy of the discontinuous Galerkin...

We present a stabilized finite element method for the scalar advection-diffusion equation, which does not require tunable mesh-dependent parameters. Stabilization is achieved by using diffusive fluxes extracted from an edge element lifting of Scharfetter-Gummel edge fluxes into the elements. Although the method is formally first-order accurate, qualitative numerical studies suggest that it occu...

Theoretically and computationally, it is possible to demonstrate that the order of accuracy of a discontinuous Galerkin (DG) solution for linear hyperbolic equations can be improved from order k+1 to 2k+1 through the use of smoothness-increasing accuracy-conserving (SIAC) filtering. However, it is a computationally complex task to perform this in an efficient manner, which becomes an even great...