Advanced boundary element methods : treatment of boundary value, transmission and contact problems /: treatment of boundary value, transmission and contact problems. (2018)

• Record Type: Book
• Further Information: Note: Joachim Gwinner, Ernst Peter Stephan.
• Authors: Gwinner, Joachim; Stephan, Ernst Peter
• Contents: Intro; Preface; Contents; 1 Introduction; 1.1 The Basic Approximation Problems; 1.2 Convergence of Projection Methods; 2 Some Elements of Potential Theory; 2.1 Representation Formulas; 2.2 Single- and Double-Layer Potential; 2.2.1 Some Remarks on Distributions; 2.2.2 Jump Relations; 2.3 Mapping Properties of Boundary Integral Operators; 2.4 Laplace's Equation in R3; 2.4.1 Representation Formula; 2.5 Calderon Projector; 2.6 Use of Complex Function Theory; 2.6.1 Representation Formula Again; 2.6.2 Applicable Representation of the Hypersingular Integral Operator; 3 A Fourier Series Approach. 4.4 Interface Problem in Linear Elasticity4.5 A Strongly Elliptic System for Exterior Maxwell's Equations; 4.5.1 A Simple Layer Procedure; 4.5.2 Modified Boundary Integral Equations; 5 The Signorini Problem and More Nonsmooth BVPs and Their Boundary Integral Formulation; 5.1 The Signorini Problem in Its Simplest Form; 5.2 A Variational Inequality of the Second Kind Modelling Unilateral Frictional Contact; 5.3 A Nonmonotone Contact Problem from Delamination; 6 A Primer to Boundary Element Methods; 6.1 Galerkin Scheme for Strongly Elliptic Operators. 6.2 Galerkin Methods for the Single-Layer Potential6.2.1 Approximation with Trigonometric Polynomials; 6.2.2 Approximation with Splines; 6.3 Collocation Method for the Single-Layer Potential; 6.4 Collocation Methods-Revisited; 6.4.1 Periodic Splines as Test and Trial Functions; 6.4.2 Convergence Theorem for Projection Methods; 6.5 BEM on Quasiuniform Meshes; 6.5.1 Periodic Polynomial Splines; 6.5.2 The Approximation Theorem; 6.5.3 Stability and Inverse Estimates; 6.5.4 Aubin-Nitsche Duality Estimateand Superapproximation; 6.5.5 Numerical Quadrature; 6.5.6 Local H( -1/2)-Error Estimates. 6.5.7 Local L2-Error Estimates6.5.8 The K-Operator-Method; 6.5.9 L(∞)-Error Estimates for the Galerkin Approximation; 6.6 A Discrete Collocation Method for Symm's Integral Equation on Curves with Corners; 6.7 Improved Galerkin Method with Augmented BoundaryElements; 6.8 Duality Estimates for Projection Methods; 6.8.1 Application to Galerkin Methods; 6.8.2 Application to Collocation Methods; 6.9 A Collocation Method Interpreted as (GM); 6.10 Modified Collocation and Qualocation; 6.11 Radial Basis Functions and Spherical Splines
• Publisher Details: Cham, Switzerland : Springer
• Publication Date: 2018
• Extent: 1 online resource
• Subjects: 515/.35; Mathematics; Boundary element methods; MATHEMATICS -- Calculus; MATHEMATICS -- Mathematical Analysis; Boundary element methods; Mathematics; Integral Equations; Numerical Analysis; Partial Differential Equations; Calculus of Variations and Optimal Control; Optimization; Mathematical and Computational Engineering; Theoretical, Mathematical and Computational Physics; Mathematics -- Number Systems; Mathematics -- Differential Equations; Mathematics -- Applied; Science -- Mathematical Physics; Numerical analysis; Differential calculus & equations; Calculus of variations; Maths for engineers; Mathematical physics; Integral equations; Numerical analysis; Differential equations, partial; Mathematical optimization; Engineering mathematics; Mathematics -- Mathematical Analysis; Integral calculus & equations; Electronic books
• Languages: English
• ISBNs: 9783319920016; 3319920014
• Related ISBNs: 9783319920009; 3319920006
• Notes: Note: Includes bibliographical references and index.; Note: Online resource; title from PDF title page (SpringerLink, viewed August 2, 2018).
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.