A streamline-diffusion method for nonconforming finite element approximations applied to convection-diffusion problems
We consider a nonconforming streamline-diffusion finite element method for solving convection-diffusion problems. The theoretical and numerical investigation for triangular and tetrahedral meshes recently given by John, Maubach and Tobiska has shown that the usual application of the SDFEM gives not...
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| Vydáno v: | Computer methods in applied mechanics and engineering Ročník 166; číslo 1; s. 85 - 97 |
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| Médium: | Journal Article |
| Jazyk: | angličtina |
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Elsevier B.V
13.11.1998
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| ISSN: | 0045-7825, 1879-2138 |
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| Abstract | We consider a nonconforming streamline-diffusion finite element method for solving convection-diffusion problems. The theoretical and numerical investigation for triangular and tetrahedral meshes recently given by John, Maubach and Tobiska has shown that the usual application of the SDFEM gives not a sufficient stabilization. Additional parameter dependent jump terms have been proposed which preserve the same order of convergence as in the conforming case. The error analysis has been essentially based on the existence of a conforming finite element subspace of the nonconforming space. Thus, the analysis can be applied for example to the Crouzeix/Raviart element but not to the nonconforming quadrilateral elements proposed by Rannacher and Turek. In this paper, parameter free new jump terms are developed which allow to handle both the triangular and the quadrilateral case. Numerical experiments support the theoretical predictions. |
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| AbstractList | We consider a nonconforming streamline-diffusion finite element method for solving convection-diffusion problems. The theoretical and numerical investigation for triangular and tetrahedral meshes recently given by John, Maubach and Tobiska has shown that the usual application of the SDFEM gives not a sufficient stabilization. Additional parameter dependent jump terms have been proposed which preserve the same order of convergence as in the conforming case. The error analysis has been essentially based on the existence of a conforming finite element subspace of the nonconforming space. Thus, the analysis can be applied for example to the Crouzeix/Raviart element but not to the nonconforming quadrilateral elements proposed by Rannacher and Turek. In this paper, parameter free new jump terms are developed which allow to handle both the triangular and the quadrilateral case. Numerical experiments support the theoretical predictions. |
| Author | Schieweck, F. John, V. Tobiska, L. Matthies, G. |
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| Cites_doi | 10.1007/BF01405198 10.1002/(SICI)1098-2426(199607)12:4<407::AID-NUM1>3.0.CO;2-Q 10.1090/S0025-5718-1987-0890252-8 10.1051/m2an/1990240202351 10.1002/num.1690080202 10.1137/0910043 10.1090/S0025-5718-97-00788-6 10.1090/S0025-5718-1986-0842120-4 10.1007/s002110050309 10.1051/m2an/1989230406271 10.1137/0733007 10.1090/S0025-5718-1993-1149289-9 |
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