Direct serendipity and mixed finite elements on convex polygons

• Published in: Numerical algorithms Vol. 92; no. 2; pp. 1451 - 1483
• Main Authors: Arbogast, Todd, Wang, Chuning
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.02.2023; Springer Nature B.V
• Subjects: Accuracy; Algebra; Algorithms; Approximation; Computer Science; Construction; Mathematical analysis; Numeric Computing; Numerical Analysis; Original Paper; Polygons; Polynomials; Serendipity; Shape functions; Theory of Computation; Direct finite elements; Serendipity finite elements; 65N12; Finite element exterior calculus; Polygonal meshes; Generalized barycentric coordinates; 65D05; Optimal approximation; 65N30

We construct new families of direct serendipity and direct mixed finite elements on general planar, strictly convex polygons that are H 1 and H (div) conforming, respectively, and possess optimal order of accuracy for any order. They have a minimal number of degrees of freedom subject to the conform...