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Stabilized Galerkin for Transient Advection of Differential Forms
(2015)Research ReportWe deal with the discretization of generalized transient advection problems for differential forms on bounded spatial domains. We pursue an Eulerian method of lines approach with explicit time-stepping. Concerning spatial discretization we extend the jump stabilized Galerkin discretization proposed in [H. Heumann and R. Hiptmair, Stabilized Galerkin methods for magnetic advection, Math. Modelling Numer. Analysis, 47 (2013), pp. 1713–1732] ...Report -
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Refined convergence theory for semi-Lagrangian schemes for pure advection
(2011)Research ReportWe consider generalized linear transient advection problems for differential forms on a bounded domain in Rn. We provide comprehensive a priori convergence estimates for their spatio-temporal discretization by means of a semi-Lagrangian approach combined with a discontinuous Galerkin method. We establish a new asymptotic estimate O(hr+1!−1 2 ) for the L2-norm of the error, where h is the spatial meshwidth, ! denotes the timestep, and r ...Report