TY - JOUR T1 - Mesh Quality and More Detailed Error Estimates of Finite Element Method AU - Yunqing Huang, Liupeng Wang & Nianyu Yi JO - Numerical Mathematics: Theory, Methods and Applications VL - 2 SP - 420 EP - 436 PY - 2017 DA - 2017/10 SN - 10 DO - http://doi.org/10.4208/nmtma.2017.s10 UR - https://global-sci.org/intro/article_detail/nmtma/12352.html KW - AB -

In this paper, we study the role of mesh quality on the accuracy of linear finite element approximation. We derive a more detailed error estimate, which shows explicitly how the shape and size of elements, and symmetry structure of mesh effect on the error of numerical approximation. Two computable parameters $G_e$ and $G_v$ are given to depict the cell geometry property and symmetry structure of the mesh. In compare with the standard a priori error estimates, which only yield information on the asymptotic error behaviour in a global sense, our proposed error estimate considers the effect of local element geometry properties, and is thus more accurate. Under certain conditions, the traditional error estimates and supercovergence results can be derived from the proposed error estimate. Moreover, the estimators $G_e$ and $G_v$ are computable and thus can be used for predicting the variation of errors. Numerical tests are presented to illustrate the performance of the proposed parameters $G_e$ and $G_v$.