Monotone Discretizations for Elliptic Second Order Partial Differential Equations
Buch in deiner Nähe kaufen
Beschreibung
This book offers a comprehensive presentation of numerical methods for elliptic boundary value problems that satisfy discrete maximum principles (DMPs). The satisfaction of DMPs ensures that numerical solutions possess physically admissible values, which is of utmost importance in numerous applications. A general framework for the proofs of monotonicity and discrete maximum principles is developed for both linear and nonlinear discretizations. Starting with the Poisson problem, the focus is on convection-diffusion-reaction problems with dominant convection, a situation which leads to a numerical problem with multi-scale character. The emphasis of this book is on finite element methods, where classical (usually linear) and modern nonlinear discretizations are presented in a unified way. In addition, popular finite difference and finite volume methods are discussed. Besides DMPs, other important properties of the methods, like convergence, are studied. Proofs are presented step by step, allowing readers to understand the analytic techniques more easily. Numerical examples illustrate the behavior of the methods.
This book offers a comprehensive presentation of numerical methods for elliptic boundary value problems that satisfy discrete maximum principles (DMPs). The satisfaction of DMPs ensures that numerical solutions possess physically admissible values, which is of utmost importance in numerous applications. A general framework for the proofs of monotonicity and discrete maximum principles is developed for both linear and nonlinear discretizations. Starting with the Poisson problem, the focus is on convection-diffusion-reaction problems with dominant convection, a situation which leads to a numerical problem with multi-scale character. The emphasis of this book is on finite element methods, where classical (usually linear) and modern nonlinear discretizations are presented in a unified way. In addition, popular finite difference and finite volume methods are discussed. Besides DMPs, other important properties of the methods, like convergence, are studied. Proofs are presented step by step, allowing readers to understand the analytic techniques more easily. Numerical examples illustrate the behavior of the methods.
First comprehensive presentation of DMP satisfying numerical methods for elliptic boundary value problems Classical linear and modern nonlinear finite element methods presented and analyzed in a unified way Detailed proofs and numerical examples provide insight into the behavior of the methods
Autor*in
Gabriel R. Barrenechea
Themen in »Monotone Discretizations for Elliptic Second Order Partial Differential Equations«
Linear Second Order Boundary Value Problems Local and Global Discrete Maximum Principles Convection-Dominated Problems Linear and Nonlinear Finite Element Methods Finite Difference and Finite Volume Methods
Stimmen zu »Monotone Discretizations for Elliptic Second Order Partial Differential Equations«
“The book is written with care and a clear didactic intention. Proofs are detailed, often at the level suitable for graduate students entering the field, while the breadth and depth of coverage will make it a standard reference for researchers working on discretisations for elliptic and convection-dominated problems. … Given the length and level of technicality, the book will be most beneficial to readers with a solid background in numerical analysis of PDEs and finite element theory.” (Denys Dutykh, Mathematical Reviews, May, 2026)
()