# Residual-Based A Posteriori Error Estimates for Symmetric Conforming Mixed Finite Elements for Linear Elasticity Problems

## TL;DR

This paper develops and verifies residual-based a posteriori error estimators for symmetric mixed finite element methods applied to linear elasticity problems, ensuring their stability and efficiency through theoretical proofs and numerical validation.

## Contribution

It introduces new a posteriori error estimators for symmetric mixed finite elements in linear elasticity, with proven stability and efficiency, supported by numerical experiments.

## Key findings

- Estimators are stable and efficient.
- Numerical examples confirm theoretical results.
- Error bounds are effectively estimated.

## Abstract

A posteriori error estimators for the symmetric mixed finite element methods for linear elasticity problems of Dirichlet and mixed boundary conditions are proposed. Stability and efficiency of the estimators are proved. Finally, we provide numerical examples to verify the theoretical results.