一般非一致网格上异质各向异性扩散问题的离散化：一种使用稳定化和混合界面的方案 (SUSHI)
Discretisation of heterogeneous and anisotropic diffusion problems on general non-conforming meshes. SUSHI: a scheme using stabilisation and hybrid interfaces
AI总结：
针对一般网格上的异质各向异性扩散问题，提出一种基于控制体中心值和内部界面未知量的离散化方案，并证明其收敛性和误差估计。
摘要：
研究并发展了一种用于一般网格上异质各向异性扩散问题的离散化方案。该方案的未知量是控制体中心的值以及某些内部界面上的值，例如可以选择在扩散张量不连续处。因此，如果不保留边未知量，该方案完全是单元中心的。通过几个数值例子表明该方案是精确的。对于一般（可能不连续）张量、一般（可能非一致）网格，且不对解的正则性作假设，得到了近似解到连续解的数学收敛性。然后在解满足足够正则性假设下，给出了误差估计。
英文摘要：
A discretisation scheme for heterogeneous anisotropic diffusion problems on general meshes is developed and studied. The unknowns of this scheme are the values at the centre of the control volumes and at some internal interfaces which may for instance be chosen at the diffusion tensor discontinuities. The scheme is therefore completely cell centred if no edge unknown is kept. It is shown to be accurate on several numerical examples. Mathematical convergence of the approximate solution to the continuous solution is obtained for general (possibly discontinuous) tensors, general (possibly non-conforming) meshes, and with no regularity assumption on the solution. An error estimate is then drawn under sufficient regularity assumptions on the solution.
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