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An H-1-Galerkin mixed finite element method for parabolic partial differential equations

DSpace at IIT Bombay

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Title An H-1-Galerkin mixed finite element method for parabolic partial differential equations
 
Creator PANI, AK
 
Subject order elliptic problems
miscible displacement
convergence analysis
helmholtz-equation
approximation
systems
parabolic initial and boundary value problem
mixed finite element method
h-1-galerkin
lbb condition
elliptic projection
semidiscrete scheme
backward euler's method
error estimates
gronwall's lemma
 
Description In this paper, an H-1-Galerkin mixed finite element method is proposed and analyzed for parabolic partial differential equations with nonselfadjoint elliptic parts. Compared to the standard H-1-Galerkin procedure, C-1-continuity for the approximating finite dimensional subspaces can be relaxed for the proposed method. Moreover, it is shown that the finite element approximations have the same rates of convergence as in the classical mixed method, but without LBB consistency condition and quasiuniformity requirement on the finite element mesh. Finally, a better rate of convergence for the flux in L-2-norm is derived using a modified H-1-Galerkin mixed method in two and three space dimensions, which confirms the findings in a single space variable and also improves upon the order of convergence of the classical mixed method under extra regularity assumptions on the exact solution.
 
Publisher SIAM PUBLICATIONS
 
Date 2011-08-29T04:21:44Z
2011-12-26T12:58:24Z
2011-12-27T05:48:15Z
2011-08-29T04:21:44Z
2011-12-26T12:58:24Z
2011-12-27T05:48:15Z
1998
 
Type Article
 
Identifier SIAM JOURNAL ON NUMERICAL ANALYSIS, 35(2), 712-727
0036-1429
http://dx.doi.org/10.1137/S0036142995280808
http://dspace.library.iitb.ac.in/xmlui/handle/10054/11956
http://hdl.handle.net/10054/11956
 
Language en