期刊
IMA JOURNAL OF NUMERICAL ANALYSIS
卷 26, 期 2, 页码 326-353出版社
OXFORD UNIV PRESS
DOI: 10.1093/imanum/dri036
关键词
anisotropic diffusion; finite-volume methods; discrete gradient; convergence analysis
Finite-volume methods for problems involving second-order operators with full diffusion matrix can be used thanks to the definition of a discrete gradient for piecewise constant functions on unstructured meshes satisfying an orthogonality condition. This discrete gradient is shown to satisfy a strong convergence property for the interpolation of regular functions, and a weak one for functions bounded in a discrete H-1-norm. To highlight the importance of both properties, the convergence of the finite-volume scheme for a homogeneous Dirichlet problem with full diffusion matrix is proven, and an error estimate is provided. Numerical tests show the actual accuracy of the method.
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