# Time-integration methods for finite element discretisations of the second-order Maxwell equation

D. Sarmany, Mikhail A. Bochev, Jacobus J.W. van der Vegt

Research output: Book/ReportReportProfessional

## Abstract

This article deals with time integration for the second-order Maxwell equations with possibly non-zero conductivity in the context of the discontinuous Galerkin finite element method DG-FEM) and the $H(\mathrm{curl})$-conforming FEM. For the spatial discretisation, hierarchic $H(\mathrm{curl})$-conforming basis functions are used up to polynomial order $p=3$ over tetrahedral meshes, meaning fourth-order convergence rate. A high-order polynomial basis often warrants the use of high-order time-integration schemes, but many well-known high-order schemes may suffer from a severe time-step stability restriction owing to the conductivity term. We investigate several possible time-integration methods from the point of view of accuracy, stability and computational work. We also carry out a numerical Fourier analysis to study the dispersion and dissipation properties of the semi-discrete DG-FEM scheme as well as the fully-discrete schemes with several of the time-integration methods. The dispersion and dissipation properties of the spatial discretisation and those of the time-integration methods are investigated separately, providing additional insight into the two discretisation steps.
Original language Undefined Enschede University of Twente, Department of Applied Mathematics 25 Published - Feb 2012

### Publication series

Name Memorandum / Department of Applied Mathematics University of Twente, Department of Applied Mathematics 1975 1874-4850 1874-4850

## Keywords

• Second-order damped Maxwell wave equation
• High-order numerical time integration
• H(curl)-conforming finite element method
• IR-79682
• METIS-285242
• Discontinuous Galerkin finite element method
• MSC-65M60
• MSC-65M20
• MSC-65L20
• MSC-65L06
• EWI-21520