The finite element method has become the most powerful approach in solving partial differential equations arising in modern engineering and physical applications. We present computation and visualisation of the solutions of some applied partial differential equations using the finite element method for most of our examples. Our examples come from solid and fluid mechanics, image processing and heat conduction in sliding meshes.

About the speaker: Dr Lamichhane was awarded the MSc in Industrial Mathematics from the University of Kaiserslautern in 2001, and the PhD in Mathematics from the University of Stuttgart in 2006. He took a postdoctoral fellow at the Australian National University in 2008 and is now a senior lecturer at the University of Newcastle. Dr Lamichhane’s main interests are numeral analysis, differential equations and applied mathematics and his recent research focus is on the approximation of solutions of partial differential equations using the finite element method.

In this talk I will briefly introduce the mixed finite element method and show their applications. I consider Poisson, elasticity, Stokes and biharmonic equations for the applications of the mixed finite element method. The mixed finite element method also arises naturally in Stokes flow, multi-physics problems as well as when we consider non-conforming discretisation techniques. I will also present my recent works on the mixed finite element method for biharmonic and Reissner-Mindlin plate equations.

The finite element method has become the most powerful approach in approximating solutions of partial differential equations arising in modern engineering and physical applications. We present some efficient finite element methods for Reissner-Mindlin, biharmonic and thin plate equations.

In the first part of the talk I present some applied partial differential equations, and introduce the finite element method using the biharmonic equation. In the second part of the talk I will discuss about the finite element method for Reissner-Mindlin, biharmonic and thin plate spline equations in a unified framework.

The Hu-Washizu formulation in elasticity is the mother of many different finite element methods in engineering computation. We present some modified Hu-Washizu formulations and their performance in removing locking effect in the nearly incompressible elasticity. The stabilisation of the standard Hu-Washizu formulation is used to obtain the stabilised nodal strain formulation or node-based uniform strain elements. However, we show that standard or stabilised nodal strain formulation should be modified to have a uniformly convergent finite element approximation in the nearly incompressible case.