Hybridizable Symmetric Stress Elements on the Barycentric Refinement in Arbitrary Dimensions

TL;DR

This paper introduces hybridizable symmetric stress elements on barycentric refined simplices in any dimension, improving the flexibility and efficiency of mixed finite element methods for linear elasticity.

Contribution

It develops a new class of hybridizable symmetric stress elements using barycentric refinement and an intrinsic tangential-normal decomposition for arbitrary dimensions and polynomial orders.

Findings

Ensures H(div)-conformity and symmetry of stress elements.

Provides stable and efficient basis functions for mixed finite element methods.

Applicable to linear elasticity problems in arbitrary dimensions.

Abstract

Hybridizable \(H(\textrm{div})\)-conforming finite elements for symmetric tensors on simplices with barycentric refinement are developed in this work for arbitrary dimensions and any polynomial order. By employing barycentric refinement and an intrinsic tangential-normal (\(t\)-\(n\)) decomposition, novel basis functions are constructed to redistribute degrees of freedom while preserving \(H(\textrm{div})\)-conformity and symmetry, and ensuring inf-sup stability. These hybridizable elements enhance computational flexibility and efficiency, with applications to mixed finite element methods for linear elasticity.