# Optimal parameter for the stabilised five-field extended Hu–Washizu formulation

## Authors

• Muhammad Ilyas University of Newcastle, Australia
• Bishnu P. Lamichhane The University of Newcastle

## Keywords:

Partial differential equation, finite element method, elasticity problem, Five-field formulation, Hu-Washizu formulation

## Abstract

We present a mixed finite element method for the elasticity problem. We expand the standard Hu–Washizu formulation to include a pressure unknown and its Lagrange multiplier. By doing so, we derive a five-field formulation. We apply a biorthogonal system that leads to an efficient numerical formulation. We address the coercivity problem by adding a stabilisation term with a parameter. We also present an analysis of the optimal choices of parameter approximation.

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Senior Lecturer

2020-08-11

## Section

Proceedings Engineering Mathematics and Applications Conference