On the error estimate of gradient inclusions

TL;DR

This paper provides an error estimate for numerical solutions of gradient inclusions in 2x2 diagonal matrices, linking the error to the number of laminations and mesh size using finite element methods.

Contribution

It introduces a general error estimate for gradient inclusions with finite laminations, reducing the problem from a compact to a finite case.

Findings

Error estimate depends on the number of laminations and mesh size

Reduction from compact to finite case simplifies analysis

Applicable to finite element methods for gradient inclusions

Abstract

The numerical analysis of gradient inclusions in a compact subset of $2\times 2$ diagonal matrices is studied. Assuming that the boundary conditions are reached after a finite number of laminations and using piecewise linear finite elements, we give a general error estimate in terms of the number of laminations and the mesh size. This is achieved by reduction results from compact to finite case.