A New Expanded Mixed Element Method for Convection-Dominated Sobolev Equation
We propose and analyze a new expanded mixed element method, whose gradient belongs to the simple square integrable space instead of the classical H(div; Ω) space of Chen’s expanded mixed element method. We study the new expanded mixed element method for convection-dominated Sobolev equation, prove t...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2014-01-01
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| Series: | The Scientific World Journal |
| Online Access: | http://dx.doi.org/10.1155/2014/297825 |
| Summary: | We propose and analyze a new expanded mixed element method, whose gradient belongs to the simple square integrable space instead of the classical H(div; Ω) space of Chen’s expanded mixed element method. We study the new expanded mixed element method for convection-dominated Sobolev equation, prove the existence and uniqueness for finite element solution, and introduce a new expanded mixed projection. We derive the optimal a priori error estimates in L2-norm for the scalar unknown u and a priori error estimates in (L2)2-norm for its gradient λ and its flux σ. Moreover, we obtain the optimal a priori error estimates in H1-norm for the scalar unknown u. Finally, we obtained some numerical results to illustrate efficiency of the new method. |
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| ISSN: | 2356-6140 1537-744X |