Monotone finite volume schemes for diffusion equations on unstructured triangular and shape-regular polygonal meshes |
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| Institution: | 1. Los Alamos National Laboratory, Theoretical Division, MS B284, Los Alamos, NM 87545, USA;2. Institute of Numerical Mathematics, Russian Academy of Sciences, 8, Gubkina, 117333 Moscow, Russia;1. Department of Mathematics, Iowa State University, Ames, IA 50011, United States;2. School of Mathematics, Physics and Information Science, Zhejiang Ocean University, Zhoushan, Zhejiang, China;3. Key Laboratory of Oceanographic Big Data Mining & Application of Zhejiang Province, Zhoushan, Zhejiang, China;1. Energy Resources Engineering, Green Earth Sciences Building, Stanford University, Stanford, CA 94305, USA;2. Chevron Energy Technology Company, 6001 Bollinger Canyon Road, San Ramon, CA 94583, USA;1. School of Mathematics and Statistics and Computational Science Hubei Key Laboratory, Wuhan University, Wuhan, Hubei 430072, PR China;2. Graduate School of China Academy of Engineering Physics, Beijing, 100088, PR China;3. Institute of Applied Physics and Computational Mathematics, Beijing 100088, PR China |
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| Abstract: | We consider a non-linear finite volume (FV) scheme for stationary diffusion equation. We prove that the scheme is monotone, i.e. it preserves positivity of analytical solutions on arbitrary triangular meshes for strongly anisotropic and heterogeneous full tensor coefficients. The scheme is extended to regular star-shaped polygonal meshes and isotropic heterogeneous coefficients. |
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