Math 604: Numerical Solution to Partial Differential Equations

·        Difference schemes for different types of partial differential equations .

·        Analysis of consistency, order, Stability and convergence

·        Introduction to finite element methods for the numerical solution to partial differential equations

·        Minimization principle

·        Weak formulation

·        Boundary conditions

·        Quadrature

·        Error Analysis, Stability, Convergence, Implementation.

·        Galerkin approximation

·        Shape Functions

·        Iso-parametric elements

·        Application to archetypal second order (heat Equation) and fourth order (Beam Equation) problems

·        Eigenvalue Problems

·        Nonlinear Problems

·        Direct and Iterative solutions of the resulting algebraic system of equations

·        Applications to the Poisson equation

·        Convection diffusion Equation