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An H-1-Galerkin mixed finite element method or an evolution equation with a positive-type memory term

DSpace at IIT Bombay

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Title An H-1-Galerkin mixed finite element method or an evolution equation with a positive-type memory term
 
Creator PANI, AK
FAIRWEATHER, G
 
Subject evolution equation
positive-type memory
mixed finite element method
h-1-galerkin
lbb condition
semidiscrete schemes
backward euler method
optimal error estimates
flux estimates
several space variables
 
Description An H-1-Galerkin mixed finite element method is analyzed for a class of evolution equations with memory. When a classical mixed method is applied to such problems, it has not been possible to obtain any estimate for the flux. However, the proposed approach yields optimal order convergence without the LBB consistency condition and quasi uniformity of the finite element mesh. Compared to the results proved for one space variable, the L-2 estimate of the flux is not optimal for problems in two and three space dimensions. Therefore, a modification of the method is proposed and analyzed. A maximum norm estimate is also derived in one and two space variables. A backward Euler approximation of the modified method is also analyzed.
 
Publisher SIAM PUBLICATIONS
 
Date 2011-08-29T04:24:32Z
2011-12-26T12:58:24Z
2011-12-27T05:48:16Z
2011-08-29T04:24:32Z
2011-12-26T12:58:24Z
2011-12-27T05:48:16Z
2002
 
Type Article
 
Identifier SIAM JOURNAL ON NUMERICAL ANALYSIS, 40(4), 1475-1490
0036-1429
http://dx.doi.org/10.1137/S0036142900372318
http://dspace.library.iitb.ac.in/xmlui/handle/10054/11957
http://hdl.handle.net/10054/11957
 
Language en