Graded Finite Element Methods for Elliptic Problems in Nonsmooth Domains

1. Auflage 2022
ISBN: 978-3-031-05820-2
Verlag: Springer Nature Switzerland

Buch, Englisch, 179 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 300 g

Reihe: Surveys and Tutorials in the Applied Mathematical Sciences

This book develops a class of graded finite element methods to solve singular elliptic boundary value problems in two- and three-dimensional domains. It provides an approachable and self-contained presentation of the topic, including both the mathematical theory and numerical tools necessary to address the major challenges imposed by the singular solution. Moreover, by focusing upon second-order equations with constant coefficients, it manages to derive explicit results that are accessible to the broader computation community. Although written with mathematics graduate students and researchers in mind, this book is also relevant to applied and computational mathematicians, scientists, and engineers in numerical methods who may encounter singular problems.

Zielgruppe

Research

Autoren/Hrsg.

Li, Hengguang

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen

Inhaltsverzeichnis

The Finite Element Method.- The Function Space.- Singularities and Graded Mesh Algorithms.- Error Estimates in Polygonal Domains.- Regularity Estimates and Graded Meshes in Polyhedral Domains.- Anisotropic Error Estimates in Polyhedral Domains.