| Titre : |
An introduction to element-based Galerkin methods on tensor-product bases : analysis, algorithms, and applications |
| Type de document : |
texte imprimé |
| Auteurs : |
Francis X. Giraldo, Auteur |
| Editeur : |
Berlin : Springer |
| Année de publication : |
2020, cop. 2020 |
| Collection : |
Texts in Computational Science and Engineering, ISSN 1611-0994 num. 24 |
| Importance : |
1 vol. (XXVI-559 p.) |
| Présentation : |
ill. en coul. |
| Format : |
24 cm |
| ISBN/ISSN/EAN : |
978-3-030-55071-4 |
| Note générale : |
PPN 265844959 |
| Langues : |
Anglais (eng) |
| Tags : |
Analyse numérique Equations aux dérivées partielles -- Solutions numériques Galerkine, Méthodes de Equations différentielles hyperboliques Équations différentielles elliptiques Numerical analysis Differential equations, Partial Numerical solutions Galerkin methods Computer science Mathematics Differential equations,Elliptic Differential equations, Hyperbolic |
| Index. décimale : |
518.028 5 Analyse numérique - Applications informatiques |
| Résumé : |
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 de contenu : |
Bibliogr. p.524-545 (424 réf.) - . Index p. 547-550 |
An introduction to element-based Galerkin methods on tensor-product bases : analysis, algorithms, and applications [texte imprimé] / Francis X. Giraldo, Auteur . - Berlin : Springer, 2020, cop. 2020 . - 1 vol. (XXVI-559 p.) : ill. en coul. ; 24 cm. - ( Texts in Computational Science and Engineering, ISSN 1611-0994; 24) . ISBN : 978-3-030-55071-4 PPN 265844959 Langues : Anglais ( eng)
| Tags : |
Analyse numérique Equations aux dérivées partielles -- Solutions numériques Galerkine, Méthodes de Equations différentielles hyperboliques Équations différentielles elliptiques Numerical analysis Differential equations, Partial Numerical solutions Galerkin methods Computer science Mathematics Differential equations,Elliptic Differential equations, Hyperbolic |
| Index. décimale : |
518.028 5 Analyse numérique - Applications informatiques |
| Résumé : |
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 de contenu : |
Bibliogr. p.524-545 (424 réf.) - . Index p. 547-550 |
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