Open AccessA Polygonal Finite Element Method for Stokes Equations
Author(s) -
Xinjiang Chen
Publication year - 2021
Publication title -
journal of advances in mathematics and computer science
Language(s) - English
Resource type - Journals
ISSN - 2456-9968
DOI - 10.9734/jamcs/2021/v36i430357
Subject(s) - barycentric coordinate system , polygon mesh , volume mesh , finite element method , mathematics , convergence (economics) , element (criminal law) , regular polygon , polygon (computer graphics) , mathematical analysis , geometry , mesh generation , computer science , physics , frame (networking) , telecommunications , political science , law , economics , thermodynamics , economic growth
In this paper, we extend the Bernardi-Raugel element [1] to convex polygonal meshes by using the generalized barycentric coordinates. Comparing to traditional discretizations defined on triangular and rectangular meshes, polygonal meshes can be more flexible when dealing with complicated domains or domains with curved boundaries. Theoretical analysis of the new element follows the standard mixed finite element theory for Stokes equations, i.e., we shall prove the discrete inf-sup condition (LBB condition) by constructing a Fortin operator. Because there is no scaling argument on polygonal meshes and the generalized barycentric coordinates are in general not polynomials, special treatments are required in the analysis. We prove that the extended Bernardi-Raugel element has optimal convergence rates. Supporting numerical results are also presented.