Minimization of energy functionals via FEM: implementation of hp-FEM

TL;DR

This paper introduces an extension of finite element methods to hp-FEM with rectangular elements in 2D for efficiently minimizing energy functionals common in science and engineering.

Contribution

The paper presents the implementation of rectangular hp-FEM in 2D, expanding previous P1 triangular element approaches for energy minimization problems.

Findings

Enhanced flexibility in finite element discretization

Improved efficiency in solving energy minimization problems

Successful extension to rectangular hp-FEM in 2D

Abstract

Many problems in science and engineering can be rigorously recast into minimizing a suitable energy functional. We have been developing efficient and flexible solution strategies to tackle various minimization problems by employing finite element discretization with P1 triangular elements [1,2]. An extension to rectangular hp-finite elements in 2D is introduced in this contribution.