Solution of 3D singular electrostatics problems using adaptive hp‐FEM

Abstract

Purpose

This paper seeks to describe the solution of a simple electrostatic problem using an adaptive hp‐FEM and to show the benefits of this approach. Numerical experiments are presented to demonstrate its superiority.

Design/methodology/approach

Adaptive hp‐FEM is used. In contrast with standard FEM, the automatic adaptivity procedure can choose from a variety of refinement candidates. An element with over estimated error can be refined in space, or its polynomial degree can be increased. Arbitrary level hanging nodes are allowed, so that no unnecessary refinements are performed in order to keep a mesh regular.

Findings

Numerical solution of a singular electrostatic problem is presented. From the comparison it can be seen that the hp‐FEM outperforms both the standard linear and quadratic elements significantly. The accuracy of an hp‐FEM solution would be hard to attain by standard means due to the limited capacity of the computer memory.

Originality/value

The paper describes results obtained from an original and innovative implementation of the adaptive hp‐FEM.

Citation

Kus, P., Solin, P. and Dolezel, I. (2008), "Solution of 3D singular electrostatics problems using adaptive hp‐FEM", COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, Vol. 27 No. 4, pp. 939-945. https://doi.org/10.1108/03321640810878360