Boundary Element Methods in Mechanics

principles, invariance under translation and fundamental solutions, integral representation theorem, finite difference methods, finite element methods, Petrov-Galerkin finite element methods and boundary element methods.Various special iterative methods for the finite difference equations are also discussed.Chapter 4: "Dissipative Systems".The numerical methods considered in Chapter 3 are revised to deal with the advection-diffusion type equations.Nonstandard methods such as upstream weighting, solution pathology at sharp fronts, and alternating direction methods are also introduced in this chapter.Chapter 5: "Nondissipative Systems" deals with transport equations such as the Euler equations, the Burger's equation, and the wave equation.Methods of characteristic, conservative finite-difference schemes, and nonstandard Galerkin finite element methods are considered.Chapter 6: "High-Order, Nonlinear, and Coupled Systems," considers special problems such as the biharmonic equation, nonlinear diffusion equations and compositional flows in porous media.The oil reservoir modeling is discussed at great length.The above list is not complete, merely representative of the topics covered in the book.