scholarly journals On A Priori Error Analysis of Fully Discrete Heterogeneous Multiscale FEM

2005 ◽  
Vol 4 (2) ◽  
pp. 447-459 ◽  
Author(s):  
Assyr Abdulle
Keyword(s):  
Error Analysis ◽  
A Priori ◽  
Fully Discrete ◽  
A Priori Error Analysis ◽  
Multiscale Fem ◽  
Heterogeneous Multiscale

ANALYSIS OF A HETEROGENEOUS MULTISCALE FEM FOR PROBLEMS IN ELASTICITY

2006 ◽  
Vol 16 (04) ◽  
pp. 615-635 ◽  
Author(s):  
ASSYR ABDULLE
Keyword(s):  
A Priori ◽  
Physical Problem ◽  
Small Cells ◽  
Macroscopic Model ◽  
Multiscale Problems ◽  
Fully Discrete ◽  
Elastic Tensor ◽  
Multiscale Fem ◽  
Priori Error Estimates ◽  
Heterogeneous Multiscale

This paper is concerned with a finite element method (FEM) for multiscale problems in linear elasticity. We propose a method which discretizes the physical problem directly by a macroscopic FEM, coupled with a microscopic FEM resolving the micro scale on small cells or patches. The assembly process of the unknown macroscopic model is done without iterative cycles. The method allows to recover the macroscopic properties of the material in an efficient and cheap way. The microscale behavior can be reconstructed from the known micro and macro solutions. We give a fully discrete convergence analysis for the proposed method which takes into account the discretization errors at both micro and macro levels. In the case of a periodic elastic tensor, we give a priori error estimates for the displacement and for the macro and micro strains and stresses as well as an error estimate for the numerical homogenized tensor.

scholarly journals An improved a priori error analysis of Nitsche’s method for Robin boundary conditions

2017 ◽  
Vol 138 (4) ◽  
pp. 1011-1026 ◽  
Author(s):  
Nora Lüthen ◽  
Mika Juntunen ◽  
Rolf Stenberg
Keyword(s):  
Error Analysis ◽  
Boundary Conditions ◽  
A Priori ◽  
Robin Boundary Conditions ◽  
Nitsche’S Method ◽  
A Priori Error Analysis ◽  
Nitsche's Method ◽  
Robin Boundary

scholarly journals A Priori Error Analysis and Spring Arithmetic

2009 ◽  
Vol 31 (3) ◽  
pp. 2214-2230 ◽  
Author(s):  
Gilles Chabert ◽  
Luc Jaulin
Keyword(s):  
Error Analysis ◽  
A Priori ◽  
A Priori Error Analysis

Time-discrete higher order ALE formulations: a priori error analysis

2013 ◽  
Vol 125 (2) ◽  
pp. 225-257 ◽  
Author(s):  
Andrea Bonito ◽  
Irene Kyza ◽  
Ricardo H. Nochetto
Keyword(s):  
Error Analysis ◽  
A Priori ◽  
Higher Order ◽  
A Priori Error Analysis
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