Error analysis of staggered finite difference finite volume schemes on unstructured meshes |
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| Authors: | Qingshan Chen |
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| Affiliation: | Department of Mathematical Sciences, Clemson University, Clemson, South Carolina |
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| Abstract: | This work combines the consistency in lower‐order differential operators with external approximations of functional spaces to obtain error estimates for finite difference finite volume schemes on unstructured nonuniform meshes. This combined approach is first applied to a one‐dimensional elliptic boundary value problem on nonuniform meshes, and a first‐order convergence rate is obtained, which agrees with the results previously reported. The approach is also applied to the staggered Marker‐and‐Cell scheme for the two‐dimensional incompressible Stokes problem on unstructured meshes. A first‐order convergence rate is obtained, which improves over a previously reported result in that it also holds on unstructured meshes. For both problems considered in this work, the convergence rate is one order higher on meshes satisfying special requirements. © 2016 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 1159–1182, 2017 |
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| Keywords: | a priori error estimate staggered‐grid finite difference finite volume incompressible Stokes Marker‐and‐Cell unstructured meshes |
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