Optimal discontinuous Galerkin methods for wave propagation
2006 (English)In: SIAM Journal on Numerical Analysis, ISSN 0036-1429, E-ISSN 1095-7170, Vol. 44, no 5, 2131-2158 p.Article in journal (Refereed) Published
We have developed and analyzed a new class of discontinuous Galerkin methods (DG) which can be seen as a compromise between standard DG and the finite element (FE) method in the way that it is explicit like standard DG and energy conserving like FE. In the literature there are many methods that achieve some of the goals of explicit time marching, unstructured grid, energy conservation, and optimal higher order accuracy, but as far as we know only our new algorithms satisfy all the conditions. We propose a new stability requirement for our DG. The stability analysis is based on the careful selection of the two FE spaces which verify the new stability condition. The convergence rate is optimal with respect to the order of the polynomials in the FE spaces. Moreover, the convergence is described by a series of numerical experiments.
Place, publisher, year, edition, pages
2006. Vol. 44, no 5, 2131-2158 p.
discontinuous Galerkin, wave propagation, optimal rate of convergence, mixed finite-elements, maxwells equations, media
IdentifiersURN: urn:nbn:se:kth:diva-16183ISI: 000242572900014OAI: oai:DiVA.org:kth-16183DiVA: diva2:334225
QC 201005252010-08-052010-08-05Bibliographically approved