Goals Theory A priori A priori error estimates N1 bound various“ measures” of u exact]-un [approximate] in terms of C(n, problem parameters h [mesh diameter, and u

Formulations Model problem Strong Formulation Find u such that Vu=f in n2 a =0 on I for a polygonal domain

Course Outline Overview of pdes(1) o Finite differences methods(6) Finite volume methods(3) Finite element methods(7) Boundary integral methods(6)

Motivation Consider a standard second order finite difference discretization

1 Background Brandt(1973)published first paper SLIDE 1 Offers the possibility of solving a problem with work and storage propor tional to the number of unknowns Well developed for elliptic proble

1 Motivation SLIDE 1 Consider a standard second order finite difference discretization of V-u= on a regular g 1.2. and 3 dimensions 1.1 1D Finite differences

Governing Equation Stability Analysis 3 Examples Relationship between σ and λh Implicit Time-Marching Scheme

Outline Governing Equation Stability Analysis 3 Examples Relationship between σ and λh Implicit Time-Marching Scheme

1 Finite difference formulas 1.1 Problem definition We have seen that one of the necessary ingredients in devising finite differe

Finite Difference Problem Definition Formulas