Interpolation and stability estimates for edge and face virtual elements of general order
Louren\c{c}o Beir\~ao da Veiga, Lorenzo Mascotto, Jian Meng
TL;DR
This paper develops interpolation error estimates and analyzes stability properties of virtual element methods of general order, which are crucial for solving electromagnetic problems in two and three dimensions.
Contribution
It introduces new interpolation error estimates and stability analysis for general order virtual elements, including both standard and serendipity types in 2D and 3D.
Findings
Interpolation error estimates for virtual elements
Stability properties of L2 discrete bilinear forms
Applicability to electromagnetic problem analysis
Abstract
We develop interpolation error estimates for general order standard and serendipity edge and face virtual elements in two and three dimensions. Contextually, we investigate the stability properties of the associated L2 discrete bilinear forms. These results are fundamental tools in the analysis of general order virtual elements, e.g., for electromagnetic problems.
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Taxonomy
TopicsElectromagnetic Simulation and Numerical Methods · Advanced Numerical Methods in Computational Mathematics · Electromagnetic Scattering and Analysis