An Introduction to Element-Based Galerkin Methods on Tensor-Product Bases: Analysis, Algorithms, and Applications

This book provides an introduction to solving partial differential equations (PDEs) numerically using element-based Galerkin methods,with a focus on tensor-product bases and covering continuous,discontinuous,and hybridized methods for hyperbolic and elliptic equations.

Format: Paperback / softback
Length: 559 pages
Publication date: 01 November 2021
Publisher: Springer Nature Switzerland AG

This comprehensive book delves into the realm of solving partial differential equations (PDEs) numerically through element-based Galerkin methods. While rooted in a strong theoretical foundation, including interpolation, numerical integration, and function spaces, its primary objective is to guide the reader in constructing and understanding these methods. Moreover, it emphasizes tensor-product bases, limiting the consideration to line elements (one dimension), quadrilateral elements (two dimensions), and cubes (three dimensions). The book covers a wide range of Galerkin methods, including continuous Galerkin methods, discontinuous Galerkin methods, and hybridized discontinuous Galerkin methods utilizing both nodal and modal basis functions. Additionally, it provides illustrative examples, which serve as valuable student projects, for tackling hyperbolic and elliptic partial differential equations, encompassing both scalar PDEs and systems of equations. By exploring these topics in depth, this book equips readers with the skills and knowledge necessary to effectively employ element-based Galerkin methods in their numerical PDE solving endeavors.

Weight: 890g
Dimension: 235 x 155 (mm)
ISBN-13: 9783030550714
Edition number: 1st ed. 2020