Finite Volume Computational Cells Discretization

Motivation The Poisson problem has a strong formulation; a minimization formulation; and a weak formulation. The minimization/weak formulations are more general than the strong formulation in terms of reqularity and admissible data

Scalar Definitions Conservation Laws

1 Scalar Conservation laws 1.1 Definit 1.1.1 Conservative form

First Order Wave Equation INITIAL BOUNDARY VALUE PROBLEM(IBVP

1 First Order ave Equation SLIDE 1 The simplest first order partial differential equation in two variables(a, t)is the linear wave equation. Recall that all first order PDE's are of hyperbolic type INITIAL BOUNDARY VALUE PROBLEM (IBVP) 0,x∈(0,1)

Background Developed over the last 25 years- Brandt (1973) published first paper with practical results Offers the possibility of solving a problem with work and storage proportional to the number of unknowns Well developed for linear elliptic problems application to other equations is still an active area of research

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