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

作者：Di Pietro Daniele A; Specogna Ruben^*

来源：Journal of Computational Physics, 2016, 326: 35-55.

DOI：10.1016/j.jcp.2016.08.041

• Electrostatics
• Computational electromagnetism
• Mixed High-Order methods
• Hybrid High-Order methods
• Discrete Geometric Approach
• Discontinuous skeletal methods
• Variable diffusion
• A posteriori error analysis

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.

• 出版日期2016-12-1