2014/09/10 by Ferenc Izsák, Izsák, Ferenc
Engineering · Mathematics · #65N12 #65N15 #65N30 #Advanced Numerical Methods in Computational Mathematics #Computational Fluid Dynamics and Aerodynamics #Differential Equations and Numerical Methods #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods in engineering
paper · pdf · doi:10.48550/arxiv.1409.2865
openalex publication_date 2014/09/10 · openalex created_date 2022/10/05 · openalex updated_date 2026/07/28
A mathematical analysis is presented for a class of interior penalty (IP)\ndiscontinuous Galerkin approximations of elliptic boundary value problems. In\nthe framework of the present theory one can derive some overpenalized IP\nbilinear forms in a natural way avoiding any heuristic choice of fluxes and\npenalty terms. The main idea is to start from bilinear forms for the local\naverage of discontinuous approximations which are rewritten using the theory of\ndistributions. It is pointed out that a class of overpenalized IP bilinear\nforms can be obtained using a lower order perturbation of these. Also, error\nestimations can be derived between the local averages of the discontinuous\napproximations and the analytic solution in the H1-seminorm. Using the local\naverages, the analysis is performed in a conforming framework without any\nassumption on extra smoothness for the solution of the original boundary value\nproblem.\n