Developing efficient finite element methods for nonlocal PDEs

Abstract

Nonlocal partial differential equations (PDE) are used to model phenomena in many fields like physics and chemistry. These models require high computational power and are difficult to solve. The purpose of this thesis is to develop efficient finite element methods for nonlocal heat and wave equations with Dirichlet boundary conditions. In this thesis, the Galerkin finite element method is used to get numerical solutions for the PDEs, and the Crank-Nicolson method is used for time discretisation. The errors for each nonlocal PDE are shown and a plot of numerical solutions is shown. The results show that the finite element can be used to efficiently model nonlocal PDEs and the errors are approximately O(h^2).