0565245 - MÚ 2024 IN eng J - Journal Article
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
R&D Projects: GA ČR(CZ) GA20-01074S
Institutional support: RVO:67985840
Keywords : numerical integration * higher dimensional finite elements * curved elements * isoparamentric elements
OECD category: Pure mathematics
Method of publishing: 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.
Permanent Link: https://hdl.handle.net/11104/0336815