Some Basic Properties of Sobolev Spaces -- Theory of Distributions -- Pseudodifferential Operators and Their Fredholm Properties -- Finite-Element Methods: Spaces and Properties -- The Potential Equation -- The Helmholtz Equation -- The Thin Plate Equation -- Linear Elastostatics -- Some Error Estimates for Numerical Solutions of Boundary Integral Equations -- Boundary Element Methods for Semilinear Elliptic Partial Differential Equations (I): The Monotone Iteration Scheme and Error Estimates -- Boundary Element Methods for Semilinear Elliptic Partial Differential Equations (II): Algorithms and Computations for Unstable Solutions from Various Models.

Boundary Element Methods have become a major numerical tool in scientific and engineering problem-solving, with particular applications to numerical computations and simulations of partial differential equations in engineering. Boundary Element Methods provides a rigorous and systematic account of the modern mathematical theory of Boundary Element Methods, including the requisite background on general partial, differential equation methods, Sobolev spaces, pseudo-differential and Fredholm operators and finite elements. It aims at the computation of many types of elliptic boundary value problems in potential theory, elasticity, wave propagation, and structural mechanics. Also presented are various methods and algorithms for nonlinear partial differential equations. This second edition has been fully revised and combines the mathematical rigour necessary for a full understanding of the subject, with extensive examples of applications illustrated with computer graphics. This book is intended as a textbook and reference for applied mathematicians, physical scientists and engineers at graduate and research level. It will be an invaluable sourcebook for all concerned with numerical modeling and the solution of partial differential equations.