Ordinary differential equation boundary value problems: 2nd-order and 4th-order spatial operators, eigenproblems. Partial differential equations: elliptic, parabolic, hyperbolic. Strong statement, weak form, minimization principle (as appropriate). Rayleigh-Ritz and Galerkin approximation. Numerical interpolation, integration, and differentiation. Finite element method for spatial discretization: formulation, bases and discrete equations, a priori and a posteriori error estimates, sparse solvers, implementation and testing. Finite difference methods for temporal discretization of mixed initial-boundary value problems. Projects focus on applications in heat transfer and structural analysis. Modest MATLAB programming: modification of open-source finite element software.
Spring 2021 Update: Fully Remote Class.