2017/06/02 by Alexandre Ern, Jean‐Luc Guermond, Ern, Alexandre +1 · 1 citation
Engineering · #Advanced Numerical Methods in Computational Mathematics #Electromagnetic Simulation and Numerical Methods #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods in engineering
paper · pdf · doi:10.48550/arxiv.1706.00600
openalex publication_date 2017/06/02 · openalex created_date 2022/09/26 · openalex updated_date 2026/07/28
We derive H\curl-error estimates and improved L2-error\nestimates for the Maxwell equations approximated using edge finite elements.\nThese estimates only invoke the expected regularity pickup of the exact\nsolution in the scale of the Sobolev spaces, which is typically lower than\n frac12 and can be arbitrarily close to 0 when the material properties are\nheterogeneous. The key tools for the analysis are commuting quasi-interpolation\noperators in H\curl- and H÷-conforming finite element\nspaces and, most crucially, newly-devised quasi-interpolation operators\ndelivering optimal estimates on the decay rate of the best-approximation error\nfor functions with Sobolev smoothness index arbitrarily close to 0. The\nproposed analysis entirely bypasses the technique known in the literature as\nthe discrete compactness argument.\n