The numerical solution of partial differential equations using the finite difference and the finite element methods. Prerequisites MATH - 6640 or departmental approval.
The course is an introduction to the finite element and finite difference methods for solving boundary-value problems (partial differential equations) and initial-value, boundary-value problems (partial differential equations). We will introduce both the finite element and finite difference methods, contrast the two and see their similarities.
We will discuss stability, consistency, and convergence of finite difference schemes, and see error estimates and convergence results for the finite element method. The students will write numerical code to solve simple partial differential equations in order to get "hands on" experience with these methods.