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An Introduction to Element-Based Galerkin Methods on Tensor-Product Bases - Analysis, Algorithms, and Applications (Hardcover, 1st ed. 2020)
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An Introduction to Element-Based Galerkin Methods on Tensor-Product Bases - Analysis, Algorithms, and Applications (Hardcover, 1st ed. 2020)
Series: Texts in Computational Science and Engineering, 24
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Total price: R2,684
Discovery Miles: 26 840
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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.
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