An Introduction to Element-Based Galerkin Methods on Tensor-Product Bases

Analysis, Algorithms, and Applications

von Francis X. Giraldo

559 Seiten, Hardcover

Kurzbeschreibung des Verlags

This book introduces the reader to solving partial differential equations (PDEs) numerically using element-based Galerkin methods. Although it draws on a solid theoretical foundation (e.g. the theory of interpolation, numerical integration, and function spaces), the book’s main focus is on how to build the method, what the resulting matrices look like, and how to write algorithms for coding Galerkin methods. In addition, the spotlight is on tensor-product bases, which means that only line elements (in one dimension), quadrilateral elements (in two dimensions), and cubes (in three dimensions) are considered. The types of Galerkin methods covered are: continuous Galerkin methods (i.e., finite/spectral elements), discontinuous Galerkin methods, and hybridized discontinuous Galerkin methods using both nodal and modal basis functions. In addition, examples are included (which can also serve as student projects) for solving hyperbolic and elliptic partial differential equations, includingboth scalar PDEs and systems of equations.

• Reihe: Texts in Computational Science and Engineering
• Themen: Mathematik und Naturwissenschaften Mathematik Mathematische Analysis, allgemein Differentialrechnung und -gleichungen
• ISBN: 9783030550684
• Sprache: Englisch
• Erscheinungsdatum: 31.10.2020
• Größe: 23.5 x 15.5 cm
• Verlag: Springer International Publishing