General theory of interpolation error estimates on anisotropic meshes
نویسندگان
چکیده
منابع مشابه
Interpolation Error Estimates for Edge Elements on Anisotropic Meshes
The classical error analysis for the Nédélec edge interpolation requires the so-called regularity assumption on the elements. However, in [18], optimal error estimates were obtained for the lowest order case, under the weaker hypothesis of the maximum angle condition. This assumption allows for anisotropic meshes that become useful, for example, for the approximation of solutions with edge sing...
متن کاملAn Interpolation Error Estimate on Anisotropic Meshes in Rn and Optimal Metrics for Mesh Refinement
In this paper, we extend the work in [W. Cao, Math. Comp., to appear] to functions of n dimensions. We measure the anisotropic behavior of higher-order derivative tensors by the “largest” (in certain sense) ellipse/ellipsoid contained in the level curve/surface of the polynomial for directional derivatives. Given the anisotropic measure for the interpolated functions, we derive an error estimat...
متن کاملInterpolation of Non-smooth Functions on Anisotropic Finite Element Meshes
In this paper, several modifications of the quasi-interpolation operator of Scott and Zhang [30] are discussed. The modified operators are defined for non-smooth functions and are suited for application on anisotropic meshes. The anisotropy of the elements is reflected in the local stability and approximation error estimates. As an application, an example is considered where anisotropic finite ...
متن کاملError estimates for Raviart-Thomas interpolation of any order on anisotropic tetrahedra
We prove optimal order error estimates for the Raviart-Thomas interpolation of arbitrary order under the maximum angle condition for triangles and under two generalizations of this condition, namely, the so-called three dimensional maximum angle condition and the regular vertex property, for tetrahedra. Our techniques are different from those used in previous papers on the subject and the resul...
متن کاملMaximum-Norm A Posteriori Error Estimates for Singularly Perturbed Reaction-Diffusion Problems on Anisotropic Meshes
Lu :“ ́ε4u` fpx, y;uq “ 0 for px, yq P Ω, u “ 0 on BΩ, (1.1) posed in a, possibly non-Lipschitz, polygonal domain Ω Ă R. Here 0 ă ε ď 1. We also assume that f is continuous on ΩˆR and satisfies fp ̈; sq P L8pΩq for all s P R, and the one-sided Lipschitz condition fpx, y;uq ́ fpx, y; vq ě Cf ru ́ vs whenever u ě v, with some constant Cf ě 0. Then there is a unique solution u PW 2 ` pΩq ĎW 1 q Ă CpΩ̄q...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Japan Journal of Industrial and Applied Mathematics
سال: 2020
ISSN: 0916-7005,1868-937X
DOI: 10.1007/s13160-020-00433-z