Mixed Discontinuous Galerkin Finite Element Method for the Biharmonic Equation
DSpace at IIT Bombay
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Title |
Mixed Discontinuous Galerkin Finite Element Method for the Biharmonic Equation
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Creator |
GUDI, T
NATARAJ, N PANI, AK |
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Subject |
boundary-value-problems
priori error analysis elliptic problems approximation hp-finite elements mixed discontinuous galerkin method biharmonic problem error estimates |
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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.
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Publisher |
SPRINGER/PLENUM PUBLISHERS
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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 |
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Type |
Article
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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 |
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Language |
en
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