Vol. 6 No. 1 (2022): Special Issue in Honor of Professor Ravi P. Agarwal
Articles

Numerical integration on higher dimensional simplicial and curved finite elements

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  • Sergey Korotov,
  • Michal Křížek
Sergey Korotov
Division of Mathematics and Physics, UKK, Mälardalen University, Box 883, 721 23 Västerås, Sweden.
Michal Křížek
Institute of Mathematics, Czech Academy of Sciences, Žitná 25, CZ–115 67 Prague 1, Czech Republic.
DOI: https://doi.org/10.26524/cm135
Published March 29, 2022
Keywords
  • numerical integration, higher dimensional finite elements, curved elements, isoparamentric elements, simplicial elements, Jacobian matrix
How to Cite
Sergey Korotov, & Michal Křížek. (2022). Numerical integration on higher dimensional simplicial and curved finite elements. Journal of Computational Mathematica, 6(1), 296 - 309. https://doi.org/10.26524/cm135

Abstract

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.

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