A posteriori error estimates are arguably more useful than a priori esti mates since we know uh. Bear in mind, however, that (i) in most methods

Finite Volume Computational Cells Discretization

Scalar Definitions Conservation Laws

First Order Wave Equation INITIAL BOUNDARY VALUE PROBLEM(IBVP

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

Outline for this Module Overview of Integral Equation Methods Important for many exterior problems (Fluids, Electromagnetics, Acoustics) Quadrature and cubature for computing integrals One and Two dimensional basics Dealing with Singularities

Outline Laplace Problems Exterior Radiation Condition Green's function Ansatz or Indirect Approach Single and Double Layer Potentials First and Second Kind Equations Greens Theorem Approach First and Second Kind Equations

1 Outline for this Module Slide 1 Overview of Integral Equation Methods Important for many exterior problems (Fluids, Electromagnetics, Acoustics) Quadrature and Cubature for computing integrals One and Two dimensional basics Dealing with Singularities 1st and 2nd Kind Integral Equations

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

Laplace Problems Exterior Radiation Condition Green’s function Ansatz or Indirect Approach Single and Double Layer Potentials First and Second Kind Equations Greens Theorem Approach First and Second Kind Equations