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

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• 作者：Daniele A. Di Pietro^a ; ^{daniele.di-pietro@umontpellier.fr" class="auth_mail" title="E-mail the corresponding author} ; Ruben Specogna^b ; ^{ruben.specogna@uniud.it" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Electrostatics ; Computational electromagnetism ; Mixed High-Order methods ; Hybrid High-Order methods ; Discrete Geometric Approach ; Discontinuous skeletal methods ; Variable diffusion ; A posteriori error analysis
• 刊名：Journal of Computational Physics
• 出版年：2016
• 出版时间：1 December 2016
• 年：2016
• 卷：326
• 期：Complete
• 页码：35-55
• 全文大小：3787 K

文摘

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.