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Difference operators from interpolating moving least squares and their deviation from optimality

Thomas Sonar (2005)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

We consider the classical Interpolating Moving Least Squares (IMLS) interpolant as defined by Lancaster and Šalkauskas [Math. Comp. 37 (1981) 141–158] and compute the first and second derivative of this interpolant at the nodes of a given grid with the help of a basic lemma on Shepard interpolants. We compare the difference formulae with those defining optimal finite difference methods and discuss their deviation from optimality.

Difference operators from interpolating moving least squares and their deviation from optimality

Thomas Sonar (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

We consider the classical Interpolating Moving Least Squares (IMLS) interpolant as defined by Lancaster and Šalkauskas [Math. Comp.37 (1981) 141–158] and compute the first and second derivative of this interpolant at the nodes of a given grid with the help of a basic lemma on Shepard interpolants. We compare the difference formulae with those defining optimal finite difference methods and discuss their deviation from optimality.

Edge-based a Posteriori Error Estimators for Generating Quasi-optimal Simplicial Meshes

A. Agouzal, K. Lipnikov, Yu. Vassilevsk (2010)

Mathematical Modelling of Natural Phenomena

We present a new method for generating a d-dimensional simplicial mesh that minimizes the Lp-norm, p > 0, of the interpolation error or its gradient. The method uses edge-based error estimates to build a tensor metric. We describe and analyze the basic steps of our method

Error estimation for finite element solutions on meshes that contain thin elements

Kenta Kobayashi, Takuya Tsuchiya (2024)

Applications of Mathematics

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 even if the shape regularity condition is violated, the standard error estimation can be obtained if ``bad'' elements that violate the shape regularity or maximum angle condition are covered virtually by simplices that satisfy the minimum angle condition. A numerical experiment illustrates the theoretical result.

Estimates for spline projections

J. H. Bramble, A. H. Schatz (1976)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

Extending Babuška-Aziz's theorem to higher-order Lagrange interpolation

Kenta Kobayashi, Takuya Tsuchiya (2016)

Applications of Mathematics

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 isosceles triangle perpendicularly does not deteriorate the optimal approximation order. We extend their technique and result to higher-order Lagrange interpolation on both triangles and tetrahedrons. To this end, we make use of difference quotients of functions with two or three variables. Then, the error estimates on squeezed...

Fast Leja points.

Baglama, J., Calvetti, D., Reichel, L. (1998)

ETNA. Electronic Transactions on Numerical Analysis [electronic only]

Currently displaying 61 – 80 of 228