Mathematical Analysis of Zienkiewicz - Zhu ' sDerivative Patch Recovery
نویسندگان
چکیده
Zienkiewicz-Zhu's derivative patch recovery technique is analyzed for general quadri-lateral nite elements. Under certain regular conditions on the meshes, the arithmetic mean of the absolute error of the recovered gradient at the nodal points is superconver-gent for the second-order elliptic operators. For rectangular meshes and the Laplacian, the recovered gradient is superconvergent in the maximum norm at the nodal points. Furthermore, it is proved for a model two-point boundary-value problem that the recovery technique results in an \ultra-convergent" derivative recovery at the nodal points for quadratic nite elements when uniform meshes are used.
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