Adaptation in coupled problems

TL;DR: In this paper, the authors address the formulation, implementation, and adaptation of closely coupled multi-physics problems with h and p-adaptive finite element methods, where a generic system of second-order differential equations is used, where the field of each individual problem is represented as an entry in the list of field variables.

Abstract: Purpose – The purpose of this paper is to address the formulation, implementation, and adaptation of closely coupled multi‐physics problems with h‐ and p‐adaptive finite element methods. A general formulation is chosen allowing for coupled problems of various types. Adaptation algorithms for h‐ and p‐refinement are given.Design/methodology/approach – A generic system of second‐order differential equations is used, where the field of each individual problem is represented as an entry in the list of field variables. Specific problems are implemented by mapping material coefficients to the coefficients of the generic form. An example with four natures is investigated with close coupling between electric, mechanical and thermal fields. h‐ and p‐refinement using a single mesh is considered, where the element order may differ for individual fields.Findings – In coupled problems, the error in each single field is affected by approximation properties of all other field quantities. In order to allow for optimal co...