An a posteriori-driven adaptive Mixed High-Order method with application to electrostatics

• Published in: Journal of computational physics Vol. 326; pp. 35 - 55
• Main Authors: Di Pietro, Daniele A., Specogna, Ruben
• Format: Journal Article
• Language: English
• Published: Elsevier Inc 01.12.2016; Elsevier
• Subjects: A posteriori error analysis; Computational electromagnetism; Discontinuous skeletal methods; Discrete Geometric Approach; Electromagnetism; Electrostatics; Engineering Sciences; Hybrid High-Order methods; Mathematics; Mixed High-Order methods; Numerical Analysis; Variable diffusion; Discontinuous skeletal methods; Computational electromagnetism; Hybrid High-Order methods; Discrete Geometric Approach; Mixed High-Order methods; Variable diffusion; A posteriori error analysis; Electrostatics; variable diffusion; computational electromagnetism; discontinuous skeletal methods; a posteriori error analysis
• ISSN: 0021-9991; 1090-2716
• DOI: 10.1016/j.jcp.2016.08.041

In this work we propose an adaptive version of the recently introduced Mixed High-Order method and showcase its performance on a comprehensive set of academic and industrial problems in computational electromagnetism. The latter include, in particular, the numerical modeling of comb-drive and MEMS devices. Mesh adaptation is driven by newly derived, residual-based error estimators. The resulting method has several advantageous features: It supports fairly general meshes, it enables arbitrary approximation orders, and has a moderate computational cost thanks to hybridization and static condensation. The a posteriori-driven mesh refinement is shown to significantly enhance the performance on problems featuring singular solutions, allowing to fully exploit the high-order of approximation.