MATH 466 Proposal Numerical Approaches of the Finite Element Method

This course introduces the finite element method (FEM) and illustrate its applicability to solving Partial Differential Equations (PDEs) by algorithm implementation and numerical experiments in MATLAB. The focus is on PDES that arise from modeling incompressible fluid flow. Topics include advanced iterative multilevel methods, computational aspects of the FEM method, discretization of saddle point problems, and applications. 2 Course Objectives: • Students will apply the finite element method to solving Partial Differential Equations (PDEs) by algorithm implementation and numerical experiments in MATLAB. • Students will write their own MATLAB programs and use them to design new algo-rithms. • Students will choose appropriate advanced iterative multilevel methods to solve, saddle point problems and related PDEs • Students will combine advanced calculus and linear algebra knowledge with scientific computing skills to solve concrete fluid flow models. • Students will conduct numerical experiments in MATLAB. • Students will write scientific reports that incorporate the design of the algorithms and programs, the mathematical justification of the design, the numerical results and their interpretation in terms of the given problem. • Students will reflect on how to apply the finite element method in other situations or contexts.