# A Least Squares Method for Linear Elasticity using A Patch Reconstructed Space

## TL;DR

This paper introduces a simple, robust, and efficient discontinuous least squares finite element method for linear elasticity, utilizing patch reconstruction with one unknown per element to achieve optimal convergence.

## Contribution

The paper presents a novel discontinuous least squares finite element method for linear elasticity using patch reconstruction, simplifying implementation and improving efficiency.

## Key findings

- Achieves optimal convergence order under energy norm.
- Demonstrates robustness and simplicity in implementation.
- Numerical results verify theoretical error estimates.

## Abstract

We propose a discontinuous least squares finite element method for solving the linear elasticity. The approximation space is obtained by patch reconstruction with only one unknown per element. We apply the L 2 norm least squares principle to the stress-displacement formulation based on discontinuous approximation with normal continuity across the interior faces. The optimal convergence order under the energy norm is attained. Numerical results of linear elasticity are presented to verify the error estimates. In addition to enjoying the advantages of discontinuous Galerkin method, we illustrate the great simplicity in implementation, the robustness and the improved efficiency of our method.