2022/01/25 by Kanghun Cho, Cho, Kanghun, Dongwoo Sheen +1
Computer Science · Engineering · Mathematics · #65N30 #Advanced Numerical Analysis Techniques #Advanced Numerical Methods in Computational Mathematics #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods for differential equations #cs.NA #math.NA #msc:65N30
paper · pdf · doi:10.48550/arxiv.2201.10652
arxiv created 2022/01/25 · openalex publication_date 2022/01/25 · arxiv updated 2022/01/27 · openalex created_date 2022/05/05 · openalex updated_date 2026/07/28
We introduce simple quadrature rules for the family of nonparametric nonconforming quadrilateral element with four degrees of freedom. Our quadrature rules are motivated by the work of Meng \it et al. \citemeng2018new. First, we introduce a family of MVP (Mean Value Property)-preserving four DOFs nonconforming elements on the intermediate reference domain introduced by Meng \it et al.. Then we design two--points and three--points quadrature rules on the intermediate reference domain. Under the assumption on equal quadrature weights, the deviation from the quadrilateral center of the Gauss points for the two points and three points rules assumes the same quadratic polynomials with constant terms modified. Thus, the two--points rule and three--points rule are constructed at one stroke. The quadrature rules are asymptotically optimal as the mesh size is sufficiently small. Several numerical experiments are carried out, which show efficiency and convergence properties of the new quadrature rules.