Adaptive stabilized mixed finite volume methods for the incompressible flow |
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| Authors: | Jian Li Zhangxin Chen Tong Zhang |
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| Affiliation: | 1. Research Center for Computational Science, Northwestern Polytechnical University, Xi'an, People's Republic of China;2. Department of Mathematics, Baoji University of Arts and Sciences, Baoji, People's Republic of China;3. Department of Chemical and Petroleum Engineering, Schulich School of Engineering, University of Calgary, 2500 University Drive N.W. Calgary, Alberta, Canada;4. Faculty of Science, Xi'an Jiaotong University, Xi'an, People's Republic of China;5. School of Mathematics and Information Science, Henan Polytechnic University, Jiaozuo, People's Republic of China |
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| Abstract: | In this article, we study adaptive stabilized mixed finite volume methods for the incompressible flows approximated using the lower order elements. A residual type of a posteriori error estimator is designed and studied with the derivation of upper and lower bounds between the exact solution and the finite volume solution. A discrete local lower bound between two successive finite volume solutions is also obtained. Also, convergence of the adaptive stabilized mixed finite volume methods is established. The presented methods have three prominent features. First, it is of practical convenience in real applications with the same partitions for velocity and pressure. Second, less computational time is required by easily applying both the lower order elements and the local grid refinement necessary for the elements of interest. Third, compared with the standard finite element method, its analysis of H1‐norm and L2‐norm for the velocity and pressure are usually derived without any high order regularity conditions on the exact solution. © 2015 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 31: 1424–1443, 2015 |
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| Keywords: | adaptive finite volume method error reduction stabilized methods Stokes equations upper and lower bounds |
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