MATH46052 | MATH66052
Intended Learning Outcomes

On completion of this course unit, students should be able to

o construct a piecewise polynomial interpolant of a functions of one variable and derive bounds on the associated approximation error;

o construct a piecewise polynomial interpolant of a function of two variables using a rectangular grid or a scattered set of sampling points and establish the degree of continuity of the resulting approximation;

o distinguish between the concepts of a weak and a classical solution of an elliptic boundary value problem and establish uniqueness of a weak solution;

o define Galerkin approximations to elliptic boundary value problems and derive a priori and a posteriori bounds for the approximation error working in standard Sobolev space norms;

o construct finite element solutions to the Poisson equation in two dimensions by using a pencil and paper and by running bespoke software;

o construct conforming finite element solutions to the biharmonic equation by using a pencil and paper and by running bespoke software