A priori error estimates for Lagrange interpolation on triangles

被引：0
作者：
Kenta Kobayashi
Takuya Tsuchiya
机构：
[1] Hitotsubashi University,Graduate School of Commerce and Management
[2] Ehime University,Graduate School of Science and Engineering
来源：
Applications of Mathematics | 2015年 / 60卷
关键词：
finite element method; Lagrange interpolation; circumradius condition; minimum angle condition; maximum angle condition; 65D05; 65N30;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
We present the error analysis of Lagrange interpolation on triangles. A new a priori error estimate is derived in which the bound is expressed in terms of the diameter and circumradius of a triangle. No geometric conditions on triangles are imposed in order to get this type of error estimates. To derive the new error estimate, we make use of the two key observations. The first is that squeezing a right isosceles triangle perpendicularly does not reduce the approximation property of Lagrange interpolation. An arbitrary triangle is obtained from a squeezed right triangle by a linear transformation. The second key observation is that the ratio of the singular values of the linear transformation is bounded by the circumradius of the target triangle.
引用
收藏
页码：485 / 499
页数：14
相关论文
共 19 条
  • [1] Babuška I.(1976)On the angle condition in the finite element method SIAM J. Numer. Anal. 13 214-226
  • [2] Aziz A. K.(2008)On the equivalence of regularity criteria for triangular and tetrahedral finite element partitions Comput. Math. Appl. 55 2227-2233
  • [3] Brandts J.(2012)The maximum angle condition is not necessary for convergence of the finite element method Numer. Math. 120 79-88
  • [4] Korotov S.(1976)Estimations d’erreur pour des éléments finis droits presque dégénérés Rev. Franc. Automat. Inform. Rech. Operat., R 10 43-60
  • [5] Křížek M.(2014)A Babuška-Aziz type proof of the circumradius condition Japan J. Ind. Appl. Math. 31 193-210
  • [6] Hannukainen A.(2015)On the circumradius condition for piecewise linear triangular elements Japan J. Ind. Appl. Math. 32 65-76
  • [7] Korotov S.(1991)On semiregular families of triangulations and linear interpolation Appl. Math., Praha 36 223-232
  • [8] Křížek M.(2010)Analysis and estimation of error constants for J. Math. Sci., Tokyo 17 27-78
  • [9] Jamet P.(1994) and Math. Comput. 63 105-119
  • [10] Kobayashi K.(1969) interpolations over triangular finite elements Apl. Mat. 14 355-376
12