On reproducing uniform flow exactly on general hexahedral cells using one degree of freedom per surface |
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Authors: | JM Nordbotten H Hægland |
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Institution: | 1. Department of Civil and Environmental Engineering, Princeton University, NJ, USA;2. Department of Mathematics, University of Bergen, Norway |
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Abstract: | The solution of second order elliptic partial differential equations typically arising for flow problems, e.g., in porous media, is frequently expressed as face fluxes of a flow field at hexahedral cells. In this letter, we show by example that the following properties are incompatible: (1) A local velocity reconstruction, (2) reproduction of uniform flow for general hexahedral cells, and (3) a flow field in H(div). This is in particular relevant to mixed finite element methods approximating H(div), and to other methods trying to reconstruct a flow field in a hexahedron using only local face fluxes, e.g., streamline tracing methods for reservoir simulation. |
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Keywords: | Uniform flow Hexahedral cells H(div) Streamline tracing Mixed finite element methods |
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