An assessment of discretizations for convection-dominated convection–diffusion equations |
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| Authors: | Matthias Augustin Alfonso Caiazzo André Fiebach Jürgen Fuhrmann Volker John Alexander Linke Rudolf Umla |
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| Affiliation: | 1. University of Kaiserslautern, Department of Mathematics, Geomathematics Group, Building 49, P.O. Box 30 49, 67653 Kaiserslautern, Germany;2. Weierstrass Institute for Applied Analysis and Stochastics, Leibniz Institute in Forschungsverbund Berlin e.V. (WIAS), Mohrenstr. 39, 10117 Berlin, Germany;3. Free University of Berlin, Department of Mathematics and Computer Science, Arnimallee 6, 14195 Berlin, Germany;4. Department of Earth Science and Engineering, South Kensington Campus, Imperial College London, SW7 2AZ, UK;1. Department of Mathematics, Ohlone College, 43600 Mission Blvd., Fremont, CA 94539, USA;2. Beijing Computational Science Research Center, Building 9, East Zone, ZPark II, No. 10 Xibeiwang East Road, Haidian District, Beijing 100193, China;3. Department of Mathematical Sciences, Kent State University at Stark, 6000 Frank Ave NW, North Canton, OH 44720, USA;1. Iowa State University, Mathematics Department, Ames, IA 50011, United States;2. Florida International University, Department of Mathematics and Statistics, Miami, FL 33199, United States;1. Department of Applied and Computational Mathematics and Statistics, University of Notre Dame, IN 46556, USA;2. Department of Mathematics, University of Pittsburgh, PA 15260, USA;3. Department of Mechanical Engineering & Materials Science, University of Pittsburgh, PA 15261, USA |
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| Abstract: | The performance of several numerical schemes for discretizing convection-dominated convection–diffusion equations will be investigated with respect to accuracy and efficiency. Accuracy is considered in measures which are of interest in applications. The study includes an exponentially fitted finite volume scheme, the Streamline-Upwind Petrov–Galerkin (SUPG) finite element method, a spurious oscillations at layers diminishing (SOLD) finite element method, a finite element method with continuous interior penalty (CIP) stabilization, a discontinuous Galerkin (DG) finite element method, and a total variation diminishing finite element method (FEMTVD). A detailed assessment of the schemes based on the Hemker example will be presented. |
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