Timeintegration methods for finite element discretisations of the secondorder Maxwell equation
Sármány, D. and Botchev, M.A. and Vegt, J.J.W. van der (2012) Timeintegration methods for finite element discretisations of the secondorder Maxwell equation. [Report]

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Abstract:  This article deals with time integration for the secondorder Maxwell equations with possibly nonzero conductivity in the context of the discontinuous Galerkin finite element method DGFEM) and the conforming FEM. For the spatial discretisation, hierarchic conforming basis functions are used up to polynomial order over tetrahedral meshes, meaning fourthorder convergence rate. A highorder polynomial basis often warrants the use of highorder timeintegration schemes, but many wellknown highorder schemes may suffer from a severe timestep stability restriction owing to the conductivity term. We investigate several possible timeintegration 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 semidiscrete DGFEM scheme as well as the fullydiscrete schemes with several of the timeintegration methods. The dispersion and dissipation properties of the spatial discretisation and those of the timeintegration methods are investigated separately, providing additional insight into the two discretisation steps. 
Item Type:  Report 
Additional information:  Devoted to the memory of Jan Verwer. Second author's surname can also be spelled as "Bochev". 
Faculty:  Electrical Engineering, Mathematics and Computer Science (EEMCS) 
Research Group:  
Link to this item:  http://purl.utwente.nl/publications/79682 
Publisher URL:  http://www.math.utwente.nl/publications 
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