MA4245 Mathematical Foundations of Galerkin Methods

Variational formulation of boundary value problems, finite element and boundary element approximations, types of elements, stability, eigenvalue problems.

Prerequisite

MA3132, MA3232 or equivalent

Lecture Hours

4

Lab Hours

0

Course Learning Outcomes

• Convergence, consistency, stability, and the Lax Equivalence theorem
• Function spaces for vectors such as Sobolev and Hilbert spaces
• Approximation of functions via Lagrange interpolation and the importance of selecting the interpolation points wisely
• Differentiation functions via Lagrange interpolation approximations
• Integration of functions and their derivatives via Lagrange interpolation
• Construction of mass, differentiation, and Laplacian matrices in weak and strong form on the reference element
• Using these reference element matrices to construct global representations
• Using the global representations of the matrices to construct approximations for partial differential equations including those in one- and two-dimensions.
• Comprehension of the differences between hyperbolic, elliptic, and parabolic partial differential equations
• Application of these methods for solving systems of linear and nonlinear partial differential equations