This book simultaneously presents the theory and the numerical treatment of elliptic boundary value problems, since an understanding of the theory is necessary for the numerical analysis of the discretisation. It first discusses the Laplace equation and its finite difference discretisation before addressing the general linear differential equation of second order. The variational formulation together with the necessary background from functional analysis provides the basis for the Galerkin and finite-element methods, which are explored in detail. A more advanced chapter leads the reader to the theory of regularity. Individual chapters are devoted to singularly perturbed as well as to elliptic eigenvalue problems. The book also presents the Stokes problem and its discretisation as an example of a saddle-point problem taking into account its relevance to applications in fluid dynamics.
Wolfgang Hackbusch
Elliptic Differential Equations
Theory and Numerical Treatment
Elliptic Differential Equations
Theory and Numerical Treatment
Ngôn ngữ Anh ● định dạng PDF ● Trang 455 ● ISBN 9783662549612 ● Kích thước tập tin 4.8 MB ● Nhà xuất bản Springer Berlin Heidelberg ● Thành phố Heidelberg ● Quốc gia DE ● Được phát hành 2017 ● Phiên bản 2 ● Có thể tải xuống 24 tháng ● Tiền tệ EUR ● TÔI 5080667 ● Sao chép bảo vệ DRM xã hội