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首页> 外文期刊>IMA Journal of Numerical Analysis >Superconvergence and extrapolation of non-conforming low order finite elements applied to the Poisson equation
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Superconvergence and extrapolation of non-conforming low order finite elements applied to the Poisson equation

机译：非相容低阶有限元的超收敛和外推应用于泊松方程

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摘要

It is well-known that on uniform meshes the piecewise linear conforming finite element solution of the Poisson equation approximates the interpolant to a higher order than the solution itself. In this paper, this type of superclose property is studied for the canonical interpolant defined by the nodal functionals of several non-conforming finite elements of lowest order. By giving explicit examples we show that some non-conforming finite elements do not admit the superclose property. In particular, we discuss two non-conforming finite elements which satisfy the superclose property. Moreover, applying a postprocessing technique, we can also state a superconvergence property for the discretization error of the postprocessed discrete solution to the solution itself. Finally, we show that an extrapolation technique leads to a further improvement of the accuracy of the finite element solution.
机译：众所周知，在均匀网格上，泊松方程的分段线性一致有限元解使插值近似于比解本身更高的阶数。在本文中，研究了由几种最低阶非合格有限元的节点函数定义的规范内插值的这种超闭合特性。通过给出显式示例，我们表明某些不符合条件的有限元不接受超闭合特性。特别是，我们讨论了两个满足超闭合特性的非协调有限元。而且，应用后处理技术，我们还可以针对后处理离散解的离散化误差向解本身陈述超收敛性质。最后，我们证明了外推技术可以进一步提高有限元解的精度。

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