An a posteriori-driven adaptive mixed high-order method with application to electrostatics

Daniele Antonio Di Pietro (1) , Ruben Specogna (2)

1 IMAG - Institut Montpelliérain Alexander Grothendieck
2 Dipartimento Politecnico di Ingegneria e Architettura

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.

Mots clés: Electrostatics; computational electromagnetism; Mixed High-Order methods; Hybrid High-Order methods; Discrete Geometric Approach; discontinuous skeletal methods; variable diffusion; a posteriori error analysis

Domaines: Analyse numérique [math.NA]; Electromagnétisme

Daniele Antonio Di Pietro, Ruben Specogna. An a posteriori-driven adaptive mixed high-order method with application to electrostatics. Journal of Computational Physics, 2016, 326, pp.35-55. ⟨10.1016/j.jcp.2016.08.041⟩. ⟨hal-01310313v2⟩