An Interpolation Error Estimate on Anisotropic Meshes in ${\mathcalR}^{n}$ and Optimal Metrics for Mesh Refinement

2007 ◽  
Vol 45 (6) ◽  
pp. 2368-2391 ◽  
Author(s):  
Weiming Cao
Keyword(s):  
Error Estimate ◽  
Mesh Refinement ◽  
Interpolation Error ◽  
Anisotropic Meshes ◽  
Interpolation Error Estimate

scholarly journals Sharp geometric requirements in the Wachspress interpolation error estimate

2018 ◽  
Vol 9 (1) ◽  
pp. 29-36
Author(s):  
Gabriel Monzón
Keyword(s):  
Aspect Ratio ◽  
Error Estimate ◽  
Edge Length ◽  
Interpolation Error ◽  
Barycentric Coordinates ◽  
Geometric Conditions ◽  
Angle Condition ◽  
Maximum Angle ◽  
Interpolation Error Estimate ◽  
Generalized Barycentric Coordinates

AbstractGeometric conditions on general polygons are given in [9] in order to guarantee the error estimate for interpolants built from generalized barycentric coordinates, and the question about identifying sharp geometric restrictions in this setting is proposed. In this work, we address the question when the construction is made by using Wachspress coordinates. We basically show that the imposed conditionsbounded aspect ratio property(barp),maximum angle condition(MAC) andminimum edge length property(melp) are actually equivalent to (MAC, melp), and if any of these conditions is not satisfied, then there is no guarantee that the error estimate is valid. In this sense, (MAC) and (melp) can be regarded as sharp geometric requirements in the Wachspress interpolation error estimate.

scholarly journals An error estimate in image processing

2012 ◽  
Vol Volume 15, 2012 ◽  
Author(s):  
Philippe Destuynder ◽  
Mohamed Jaoua ◽  
Hela Sellami
Keyword(s):  
Finite Element Method ◽  
Image Processing ◽  
Finite Element ◽  
Error Estimate ◽  
Linear Formulation ◽  
Interpolation Error ◽  
Restoration Algorithm ◽  
Non Linear ◽  
International Audience ◽  
Interpolation Error Estimate

International audience A new interpolation error estimate for a finite element method for image processing is proved in this paper. The suggested scheme is based on the Raviart-Thomas one, extended to a non linear formulation. The numerical trials run confirm the accuracy of the restoration algorithm.

Interpolation error estimates for edge elements on anisotropic meshes

2011 ◽  
Vol 31 (4) ◽  
pp. 1683-1712
Author(s):  
A. L. Lombardi
Keyword(s):  
Error Estimates ◽  
Interpolation Error ◽  
Edge Elements ◽  
Anisotropic Meshes

On generalized binomial laws to evaluate finite element accuracy: preliminary probabilistic results for adaptive mesh refinement

2020 ◽  
Vol 28 (2) ◽  
pp. 63-74
Author(s):  
Joël Chaskalovic ◽  
Franck Assous
Keyword(s):  
Finite Element ◽  
Finite Elements ◽  
Error Estimate ◽  
Adaptive Mesh Refinement ◽  
Mesh Refinement ◽  
Adaptive Mesh ◽  
Random Variable ◽  
Geometrical Interpretation ◽  
Relative Accuracy ◽  
Probabilistic Methods

AbstractThe aim of this paper is to provide new perspectives on the relative finite elements accuracy. Starting from a geometrical interpretation of the error estimate which can be deduced from Bramble–Hilbert lemma, we derive a probability law that evaluates the relative accuracy, considered as a random variable, between two finite elements Pk and Pm, k < m. We extend this probability law to get a cumulated probabilistic law for two main applications. The first one concerns a family of meshes, the second one is dedicated to a sequence of simplexes constituting a given mesh. Both of these applications could be considered as a first step toward application for adaptive mesh refinement with probabilistic methods.

scholarly journals General theory of interpolation error estimates on anisotropic meshes

2020 ◽  
Author(s):  
Hiroki Ishizaka ◽  
Kenta Kobayashi ◽  
Takuya Tsuchiya
Keyword(s):  
General Theory ◽  
Error Estimates ◽  
Interpolation Error ◽  
Anisotropic Meshes
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