@book{198609edc7b347f0aff84ae76a091621,

title = "Time-integration methods for finite element discretisations of the second-order Maxwell equation",

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.",

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",

author = "D. Sarmany and Bochev, {Mikhail A.} and {van der Vegt}, {Jacobus J.W.}",

note = "Devoted to the memory of Jan Verwer. Second author's surname can also be spelled as {"}Bochev{"}.",

year = "2012",

month = feb,

language = "Undefined",

series = "Memorandum / Department of Applied Mathematics",

publisher = "University of Twente, Department of Applied Mathematics",

number = "1975",

}