Numerical integration on higher dimensional simplicial and curved finite elements

0565245 - MÚ 2024 IN eng J - Článek v odborném periodiku
Korotov, S. - Křížek, Michal
Numerical integration on higher dimensional simplicial and curved finite elements.
Journal of Computational Mathematica. Roč. 6, č. 1 (2022), s. 296-309. E-ISSN 2456-8686
Grant CEP: GA ČR(CZ) GA20-01074S
Institucionální podpora: RVO:67985840
Klíčová slova: numerical integration * higher dimensional finite elements * curved elements * isoparamentric elements
Obor OECD: Pure mathematics
Způsob publikování: Open access
https://doi.org/10.26524/cm135

We present a formula which evaluates lower degree monomials over higher dimensional simplices by means of integration of higher degree monomials over an interval, triangle or tetrahedron. Further, we show how to apply some higher order quadrature formulae on curved elements using a one-to-one mapping from the reference simplicial element to a curved element.Finally, we demonstrate that the non-zero Jacobian does not imply that this mapping is one-to-one.
Trvalý link: https://hdl.handle.net/11104/0336815