2019/08/22 by Mathias Anselmann, Markus Bause, Anselmann, Mathias +5 · 2 citations
Engineering · Mathematics · #35L05 #65M12 #65M60 #Electromagnetic Simulation and Numerical Methods #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods for differential equations #Numerical methods in engineering
paper · pdf · doi:10.48550/arxiv.1908.08238
openalex publication_date 2019/08/22 · openalex created_date 2022/07/28 · openalex updated_date 2026/07/28
We introduce and analyze a class of Galerkin-collocation discretization\nschemes in time for the wave equation. Its conceptual basis is the\nestablishment of a direct connection between the Galerkin method for the time\ndiscretization and the classical collocation methods, with the perspective of\nachieving the accuracy of the former with reduced computational costs provided\nby the latter in terms of less complex linear algebraic systems. Continuously\ndifferentiable in time discrete solutions are obtained by the application of a\nspecial quadrature rule involving derivatives. Optimal order error estimates\nare proved for fully discrete approximations based on the Galerkin-collocation\napproach. Further, the concept of Galerkin-collocation approximation is\nextended to twice continuously differentiable in time discrete solutions. A\ndirect connection between the two families by a computationally cheap\npost-processing is presented. The error estimates are illustrated by numerical\nexperiments.\n