Multiscale asymptotic expansion and finite element methods for the mixed boundary value problems of second order elliptic equation in perforated domains

2006 ◽  
Vol 103 (1) ◽  
pp. 11-45 ◽  
Author(s):  
Li-Qun Cao
Keyword(s):  
Finite Element ◽  
Asymptotic Expansion ◽  
Elliptic Equation ◽  
Boundary Value Problems ◽  
Finite Element Methods ◽  
Mixed Boundary ◽  
Boundary Value ◽  
Order Elliptic Equation ◽  
Perforated Domains ◽  
Second Order Elliptic Equation

scholarly journals Boundary problem with integral displacement for the model equation of elliptic type

2020 ◽  
pp. 65-74
Author(s):  
З.А. Нахушева
Keyword(s):  
Elliptic Equation ◽  
Boundary Value Problems ◽  
Boundary Problem ◽  
Model Equation ◽  
Boundary Value ◽  
Nonlocal Boundary ◽  
Elliptic Type ◽  
Order Elliptic Equation ◽  
Local Boundary ◽  
Second Order Elliptic Equation

Для модельного эллиптического уравнения второго порядка рассматривается метод редукции нелокальных краевых задач с интегральным смещением к локальным краевым задачам для уравнения более высокого порядка составного типа. Исследуется разрешимость поставленных задач. For a model second order elliptic equation is considered the method of reduction of nonlocal boundary value problems with integral offset to the local boundary value problems for equations of higher order composite type. The solvability of tasks is investigated.

General non local boundary value problem for second order elliptic equation

2018 ◽  
Vol 291 (10) ◽  
pp. 1470-1485
Author(s):  
Aissa Aibeche ◽  
Nasreddine Amroune ◽  
Stephane Maingot
Keyword(s):  
Elliptic Equation ◽  
Boundary Value Problem ◽  
Boundary Value ◽  
Second Order ◽  
Order Elliptic Equation ◽  
Local Boundary ◽  
Second Order Elliptic Equation ◽  
Non Local

ASYMPTOTIC EXPANSION AND CONVERGENCE THEOREM OF CONTROL AND OBSERVATION ON THE BOUNDARY FOR SECOND-ORDER ELLIPTIC EQUATION WITH HIGHLY OSCILLATORY COEFFICIENTS

2004 ◽  
Vol 14 (03) ◽  
pp. 417-437 ◽  
Author(s):  
LI-QUN CAO
Keyword(s):  
Asymptotic Expansion ◽  
Elliptic Equation ◽  
Asymptotic Expansions ◽  
Convergence Theorem ◽  
Second Order ◽  
Order Elliptic Equation ◽  
Oscillating Coefficients ◽  
Highly Oscillatory ◽  
Second Order Elliptic Equation ◽  
The Neumann Problem

In this paper, we shall study systems governed by the Neumann problem of second-order elliptic equation with rapidly oscillating coefficients and with control and observations on the boundary. The multiscale asymptotic expansions of the solution for considering problem in the case without any constraints, and homogenized equation in the case with constraints will be given, their rigorous proofs will also be proposed.

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