Minimization of p-Laplacian via the Finite Element Method in MATLAB

TL;DR

This paper presents a MATLAB implementation for minimizing p-Laplacian energy functionals using finite element discretization and trust-region optimization, emphasizing efficient gradient evaluation and Hessian sparsity in 1D and 2D.

Contribution

It introduces a vectorized MATLAB approach for solving p-Laplace problems that can be adapted to various energy formulations, combining finite element discretization with trust-region methods.

Findings

Efficient MATLAB implementation for p-Laplacian minimization.

Effective use of gradient evaluation and Hessian sparsity.

Applicable to multiple dimensions and energy formulations.

Abstract

Minimization of energy functionals is based on a discretization by the finite element method and optimization by the trust-region method. A key tool is a local evaluation of the approximated gradients together with sparsity of the resulting Hessian matrix. We describe a vectorized MATLAB implementation of the p-Laplace problem in one and two space-dimensions, however it is easily applicable to other energy formulations.