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Mixed Discontinuous Galerkin Finite Element Method for the Biharmonic Equation

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Title Mixed Discontinuous Galerkin Finite Element Method for the Biharmonic Equation
 
Creator GUDI, T
NATARAJ, N
PANI, AK
 
Subject boundary-value-problems
priori error analysis
elliptic problems
approximation
hp-finite elements
mixed discontinuous galerkin method
biharmonic problem
error estimates
 
Description In this paper, we first split the biharmonic equation Delta(2)u = f with nonhomogeneous essential boundary conditions into a system of two second order equations by introducing an auxiliary variable v = Delta u and then apply an hp-mixed discontinuous Galerkin method to the resulting system. The unknown approximation v(h) of v can easily be eliminated to reduce the discrete problem to a Schur complement system in u(h), which is an approximation of u. A direct approximation vh of v can be obtained from the approximation uh of u. Using piecewise polynomials of degree p = 3, a priori error estimates of u - u(h) in the broken H-1 norm as well as in L-2 norm which are optimal in h and suboptimal in p are derived. Moreover, a priori error bound for v - v(h) in L-2 norm which is suboptimal in h and p is also discussed. When p = 2, the preset method also converges, but with suboptimal convergence rate. Finally, numerical experiments are presented to illustrate the theoretical results.
 
Publisher SPRINGER/PLENUM PUBLISHERS
 
Date 2011-08-30T14:34:05Z
2011-12-26T12:59:00Z
2011-12-27T05:49:49Z
2011-08-30T14:34:05Z
2011-12-26T12:59:00Z
2011-12-27T05:49:49Z
2008
 
Type Article
 
Identifier JOURNAL OF SCIENTIFIC COMPUTING, 37(2), 139-161
0885-7474
http://dx.doi.org/10.1007/s10915-008-9200-1
http://dspace.library.iitb.ac.in/xmlui/handle/10054/12353
http://hdl.handle.net/10054/12353
 
Language en