(untitled) (Journal of Computational Mathematics, 2022)
In this paper, we construct an H^1-conforming quadratic finite element on convex polygonal meshes using the generalized barycentric coordinates. The element has optimal approximation rates. Using this quadratic element, two stable discretizations for the Stokes equations are developed, which can be viewed as the extensions of the P_2-P_0 and the Q_2-(discontinuous)P_1 elements, respectively, to polygonal meshes. Numerical results are presented, which support our theoretical claims.