General theory of interpolation error estimates on anisotropic meshes

2020/02/22 by Ishizaka, Hiroki, Kobayashi, Kenta, Tsuchiya, Takuya · 1 citation
#FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.2002.09721

Abstract

We propose a general theory of estimating interpolation error for smooth functions in two and three dimensions. In our theory, the error of interpolation is bound in terms of the diameter of a simplex and a geometric parameter. In the two-dimensional case, our geometric parameter is equivalent to the circumradius of a triangle. In the three-dimensional case, our geometric parameter also represents the flatness of a tetrahedron. Through the introduction of the geometric parameter, the error estimates newly obtained can be applied to cases that violate the maximum-angle condition.

Cited by

• On discrete Sobolev inequalities for nonconforming finite elements under a semi-regular mesh condition

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