Recurrences for Quadrilateral High-Order Finite Elements
High order finite element methods (FEM) are well established numerical techniques for solving partial differential equations on complicated domains. In particular, if the unknown solution is smooth, using polynomial basis functions of higher degree speeds up the numerical solution significantly. At...
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| Veröffentlicht in: | Mathematics in computer science 2022-12, Vol.16 (4), Article 32 |
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| creator | Beuchler, Sven Haubold, Tim Pillwein, Veronika |
| description | High order finite element methods (FEM) are well established numerical techniques for solving partial differential equations on complicated domains. In particular, if the unknown solution is smooth, using polynomial basis functions of higher degree speeds up the numerical solution significantly. At the same time, the computations get much more involved and any simplification, such as efficient recurrence relations, are most welcome. Recently, computer algebra algorithms have been applied to improve FEMs in several ways. In this note, we present a symbolic approach to an issue occuring when working with quadrilateral elements. |
| doi_str_mv | 10.1007/s11786-022-00547-2 |
| format | Article |
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| subjects | Algorithms Basis functions Computer algebra Computer Science Finite element method Mathematical analysis Mathematics Mathematics and Statistics Partial differential equations Polynomials Quadrilaterals |
| title | Recurrences for Quadrilateral High-Order Finite Elements |
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