A Novel Characteristic Expanded Mixed Method for Reaction-Convection-Diffusion Problems
A novel characteristic expanded mixed finite element method is proposed and analyzed for reaction-convection-diffusion problems. The diffusion term ∇·(a(x,t)∇u) is discretized by the novel expanded mixed method, whose gradient belongs to the square integrable space instead of the classical H(div;Ω)...
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| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2013/683205 |
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| _version_ | 1849306856273477632 |
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| author | Yang Liu Hong Li Wei Gao Siriguleng He Zhichao Fang |
| author_facet | Yang Liu Hong Li Wei Gao Siriguleng He Zhichao Fang |
| author_sort | Yang Liu |
| collection | DOAJ |
| description | A novel characteristic expanded mixed finite element method is proposed and analyzed for reaction-convection-diffusion problems. The diffusion term ∇·(a(x,t)∇u) is discretized by the novel expanded mixed method, whose gradient belongs to the square integrable space instead of the classical H(div;Ω) space and the hyperbolic part d(x)(∂u/∂t)+c(x,t)·∇u is handled by the characteristic method. For a priori error estimates, some important lemmas based on the novel expanded mixed projection are introduced. The fully discrete error estimates based on backward Euler scheme are obtained. Moreover, the optimal a priori error estimates in L2- and H1-norms for the scalar unknown u and a priori error estimates in (L2)2-norm for its gradient λ and its flux σ (the coefficients times the negative gradient) are derived. Finally, a numerical example is provided to verify our theoretical results. |
| format | Article |
| id | doaj-art-1eddde46f03c43ee85b614c5aa865ec9 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-1eddde46f03c43ee85b614c5aa865ec92025-08-20T03:54:57ZengWileyJournal of Applied Mathematics1110-757X1687-00422013-01-01201310.1155/2013/683205683205A Novel Characteristic Expanded Mixed Method for Reaction-Convection-Diffusion ProblemsYang Liu0Hong Li1Wei Gao2Siriguleng He3Zhichao Fang4School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, ChinaSchool of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, ChinaSchool of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, ChinaSchool of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, ChinaSchool of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, ChinaA novel characteristic expanded mixed finite element method is proposed and analyzed for reaction-convection-diffusion problems. The diffusion term ∇·(a(x,t)∇u) is discretized by the novel expanded mixed method, whose gradient belongs to the square integrable space instead of the classical H(div;Ω) space and the hyperbolic part d(x)(∂u/∂t)+c(x,t)·∇u is handled by the characteristic method. For a priori error estimates, some important lemmas based on the novel expanded mixed projection are introduced. The fully discrete error estimates based on backward Euler scheme are obtained. Moreover, the optimal a priori error estimates in L2- and H1-norms for the scalar unknown u and a priori error estimates in (L2)2-norm for its gradient λ and its flux σ (the coefficients times the negative gradient) are derived. Finally, a numerical example is provided to verify our theoretical results.http://dx.doi.org/10.1155/2013/683205 |
| spellingShingle | Yang Liu Hong Li Wei Gao Siriguleng He Zhichao Fang A Novel Characteristic Expanded Mixed Method for Reaction-Convection-Diffusion Problems Journal of Applied Mathematics |
| title | A Novel Characteristic Expanded Mixed Method for Reaction-Convection-Diffusion Problems |
| title_full | A Novel Characteristic Expanded Mixed Method for Reaction-Convection-Diffusion Problems |
| title_fullStr | A Novel Characteristic Expanded Mixed Method for Reaction-Convection-Diffusion Problems |
| title_full_unstemmed | A Novel Characteristic Expanded Mixed Method for Reaction-Convection-Diffusion Problems |
| title_short | A Novel Characteristic Expanded Mixed Method for Reaction-Convection-Diffusion Problems |
| title_sort | novel characteristic expanded mixed method for reaction convection diffusion problems |
| url | http://dx.doi.org/10.1155/2013/683205 |
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