UID:
almahu_9948609783602882
Format:
XXVI, 559 p. 171 illus., 168 illus. in color.
,
online resource.
Edition:
1st ed. 2020.
ISBN:
9783030550691
Series Statement:
Texts in Computational Science and Engineering, 24
Content:
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, including both scalar PDEs and systems of equations.
Note:
Introduction -- Motivation and Background -- Overview of Existing Methods -- One-Dimensional Problems -- Interpolation in One Dimension -- Numerical Integration in One Dimension -- 1D Continuous Galerkin Method for Hyperbolic Equations -- 1D Discontinuous Galerkin Methods for Hyperbolic Equations -- 1D Unified Continuous and Discontinuous Galerkin Methods for Systems of Hyperbolic Equations -- 1D Continuous Galerkin Methods for Elliptic Equations -- 1D Discontinuous Galerkin Methods for Elliptic Equations -- Two-Dimensional Problems -- Interpolation in Multiple Dimensions -- Numerical Integration in Multiple Dimensions -- 2D Continuous Galerkin Methods for Elliptic Equations -- 2D Discontinuous Galerkin Methods for Elliptic Equations -- 2D Unified Continuous and Discontinuous Galerkin Methods for Elliptic Equations -- 2D Continuous Galerkin Methods for Hyperbolic Equations -- 2D Discontinuous Galerkin Methods for Hyperbolic Equations -- 2D Continuous/Discontinuous Galerkin Methods for Hyperbolic Equations -- Advanced Topics -- Stabilization of High-Order Methods -- Adaptive Mesh Refinement -- Time Integration -- 1D Hybridizable Discontinuous Galerkin Method -- Classification of Partial Differential Equations and Vector Notation -- Jacobi Polynomials -- Data Structures.
In:
Springer Nature eBook
Additional Edition:
Printed edition: ISBN 9783030550684
Additional Edition:
Printed edition: ISBN 9783030550707
Additional Edition:
Printed edition: ISBN 9783030550714
Language:
English
DOI:
10.1007/978-3-030-55069-1
URL:
https://doi.org/10.1007/978-3-030-55069-1
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