1 Scalar Conservation laws 1.1 Definit 1.1.1 Conservative form

First Order Wave Equation INITIAL BOUNDARY VALUE PROBLEM(IBVP

Integral Equation Methods Reminder about galerkin and Collocation Example of convergence issues in 1D First and second kind integral equations Develop some intuition about the difficulties Convergence for second kind equations Consistency and stability issues

Easy technique for computing integrals Piecewise constant approach sian Quadra Convergence pI ssential role of orthogonal polynomials Multidimensional Integra Techniques for singular kernels Adapt ation and variable transformation Singular quadrature

Integral Equation Methods Reminder about Galerkin and collocation Example of convergence issues in 1D First and second kind integral equations Develop some intuition about the difficulties Convergence for second kind equations Consistency and stability issues Nystrom Method

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