A residual a posteriori error estimate for partition of unity finite elements for three‐dimensional transient heat diffusion problems using multiple global enrichment functions

2020 ◽  
Vol 121 (12) ◽  
pp. 2727-2746 ◽  
Author(s):  
Muhammad Iqbal ◽  
Heiko Gimperlein ◽  
Omar Laghrouche ◽  
Khurshid Alam ◽  
M. Shadi Mohamed ◽  
...  
Keyword(s):  
Three Dimensional ◽  
Partition Of Unity ◽  
Posteriori Error ◽  
A Posteriori Error Estimate ◽  
Heat Diffusion ◽  
Posteriori Error Estimate ◽  
A Posteriori ◽  
A Posteriori Error ◽  
Transient Heat Diffusion ◽  
Diffusion Problems

A multiscale a posteriori error estimate

2005 ◽  
Vol 194 (18-20) ◽  
pp. 2077-2094 ◽  
Author(s):  
Rodolfo Araya ◽  
Frédéric Valentin
Keyword(s):  
Error Estimate ◽  
Posteriori Error ◽  
A Posteriori Error Estimate ◽  
Posteriori Error Estimate ◽  
A Posteriori ◽  
A Posteriori Error

A HIERARCHICAL A POSTERIORI ERROR ESTIMATE FOR AN ADVECTION-DIFFUSION-REACTION PROBLEM

2005 ◽  
Vol 15 (07) ◽  
pp. 1119-1139 ◽  
Author(s):  
RODOLFO ARAYA ◽  
ABNER H. POZA ◽  
ERNST P. STEPHAN
Keyword(s):  
Error Estimate ◽  
Posteriori Error ◽  
A Posteriori Error Estimate ◽  
Diffusion Reaction ◽  
Posteriori Error Estimate ◽  
A Posteriori ◽  
A Posteriori Error ◽  
Advection Diffusion ◽  
Norm Of The Error ◽  
Reaction Problem

In this work we introduce a new a posteriori error estimate of hierarchical type for the advection-diffusion-reaction equation. We prove the equivalence between the energy norm of the error and our error estimate using an auxiliary linear problem for the residual and an easy way to prove inf–sup condition.

Solution of the inverse elastography problem for parametric classes of inclusions with a posteriori error estimate

2018 ◽  
Vol 26 (4) ◽  
pp. 493-499 ◽  
Author(s):  
Alexander S. Leonov ◽  
Alexander N. Sharov ◽  
Anatoly G. Yagola
Keyword(s):  
Error Estimate ◽  
Young’S Modulus ◽  
Young's Modulus ◽  
Posteriori Error ◽  
Theory Of Elasticity ◽  
A Posteriori Error Estimate ◽  
Posteriori Error Estimate ◽  
A Posteriori ◽  
Unknown Parameters ◽  
A Posteriori Error

Abstract This article presents the solution of a special inverse elastography problem: knowing vertical displacements of compressed biological tissue to find a piecewise constant distribution of Young’s modulus in an investigated specimen. Our goal is to detect homogeneous inclusions in the tissue, which can be interpreted as oncological. To this end, we consider the specimen as two-dimensional elastic solid, displacements of which satisfy the differential equations of the linear static theory of elasticity in the plain strain statement. The inclusions to be found are specified by parametric functions with unknown geometric parameters and unknown Young’s modulus. Reducing this inverse problem to the search for all unknown parameters, we solve it applying the modified method of extending compacts by V. K. Ivanov and I. N. Dombrovskaya. A posteriori error estimate is carried out for the obtained approximate solutions.

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