TY - JOUR
T1 - Explicit Error Estimates for Mixed and Nonconforming Finite Elements
AU - Mao , Shipeng
AU - Shi , Zhongci
JO - Journal of Computational Mathematics
VL - 4
SP - 425
EP - 440
PY - 2009
DA - 2009/08
SN - 27
DO - http://doi.org/10.4208/jcm.2009.27.4.011
UR - https://global-sci.org/intro/article_detail/jcm/8581.html
KW - Mixed finite element, Nonconforming finite element, Explicit error estimate,
Maximal angle condition.
AB - <p style="text-align: justify;">In this paper, we study the explicit expressions of the constants in the error estimates of the lowest order mixed and nonconforming finite element methods. We start with an explicit relation between the error constant of the lowest order Raviart-Thomas interpolation error and the geometric characters of the triangle. This gives an explicit error constant of the lowest order mixed finite element method. Furthermore, similar results can be extended to the nonconforming&nbsp;$P_1$ scheme based on its close connection with the lowest order Raviart-Thomas method. Meanwhile, such explicit a priori error estimates can be used as computable error bounds, which are also consistent with the maximal angle condition for the optimal error estimates of mixed and nonconforming finite element methods.</p>