27 citations · 79 across the 17 of their papers we have counts for
15 papers · 1 filter
Remarkable upper bounds for interpolation error constants on triangles
Kenta Kobayashi
We introduce remarkable upper bounds, which are sharp and given by simple formulas, for the interpolation error constants on triangles. These constants are crucial for analyzing in…
Error estimation for finite element method on meshes that contain thin elements
Kenta Kobayashi, Takuya Tsuchiya
In an error estimation of finite element solutions to the Poisson equation, we usually impose the shape regularity assumption on the meshes to be used. In this paper, we show that…
Anisotropic interpolation error estimates using a new geometric parameter
Hiroki Ishizaka, Kenta Kobayashi, Takuya Tsuchiya
We present precise anisotropic interpolation error estimates for smooth functions using a new geometric parameter and derive inverse inequalities on anisotropic meshes. In our theo…
Lectures on error analysis of interpolation on simplicial triangulations without the shape-regularity assumption, Part 2: Lagrange interpolation on tetrahedrons
Kenta Kobayashi, Takuya Tsuchiya
This is the second lecture note on the error analysis of interpolation on simplicial elements without the shape regularity assumption (the previous one is arXiv:1908.03894). In thi…
A new geometric condition equivalent to the maximum angle condition for tetrahedrons
Hiroki Ishizaka, Kenta Kobayashi, Ryo Suzuki +1
For a tetrahedron, suppose that all internal angles of faces and all dihedral angles are less than a fixed constant that is smaller than . Then, it is said to satisfy the ma…
Crouzeix-Raviart and Raviart-Thomas finite-element error analysis on anisotropic meshes violating the maximum-angle condition
Hiroki Ishizaka, Kenta Kobayashi, Takuya Tsuchiya
We investigate the piecewise linear nonconforming Crouzeix-Raviar and the lowest order Raviart-Thomas finite-element methods for the Poisson problem on three-dimensional anisotropi…
General theory of interpolation error estimates on anisotropic meshes
Hiroki Ishizaka, Kenta Kobayashi, Takuya Tsuchiya
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 d…
Lectures on error analysis of interpolation on simplicial triangulations without the shape-regularity assumption Part 1: Lagrange interpolation on triangles
Kenta Kobayashi, Takuya Tsuchiya
In the error analysis of finite element methods, the shape regularity assumption on triangulations is typically imposed to obtain a priori error estimations. In practical computati…
Error analysis of Crouzeix-Raviart and Raviart-Thomas finite element methods
Kenta Kobayashi, Takuya Tsuchiya
We discuss the error analysis of the lowest degree Crouzeix-Raviart and Raviart-Thomas finite element methods applied to a two-dimensional Poisson equation. To obtain error estimat…
Approximating surface areas by interpolations on triangulations
Kenta Kobayashi, Takuya Tsuchiya
We consider surface area approximations by Lagrange and Crouzeix--Raviart interpolations on triangulations. For Lagrange interpolation, we give an alternative proof for Young's cla…
Error Analysis of Lagrange Interpolation on Tetrahedrons
Kenta Kobayashi, Takuya Tsuchiya
This paper describes the analysis of Lagrange interpolation errors on tetrahedrons. In many textbooks, the error analysis of Lagrange interpolation is conducted under geometric ass…
Extenting of Babuška-Aziz's theorem to higher-order Lagrange interpolation
Kenta Kobayashi, Takuya Tsuchiya
We consider the error analysis of Lagrange interpolation on triangles and tetrahedrons. For Lagrange interpolation of order one, Babuška and Aziz showed that squeezing a right isos…
A priori error estimates for Lagrange interpolation on triangles
Kenta Kobayashi, Takuya Tsuchiya
We present the error analysis of Lagrange interpolation on triangles. A new \textit{a priori} error estimate is derived in which the bound is expressed in terms of the diameter and…
On the circumradius condition for piecewise linear triangular elements
Kenta Kobayashi, Takuya Tsuchiya
We discuss the error analysis of linear interpolation on triangular elements. We claim that the circumradius condition is more essential then the well-known maximum angle condition…
A Babuška-Aziz type proof of the circumradius condition
Kenta Kobayashi, Takuya Tsuchiya
In this paper the error of polynomial interpolation of degree 1 on triangles is considered. The circumradius condition, which is more general than the maximum angle condition, is e…