Direct serendipity and mixed finite elements on convex polygons

DOI10.1007/S11075-022-01348-1OpenAlexW4221146165WikidataQ114224264 ScholiaQ114224264MaRDI QIDQ2679833

Todd Arbogast, Chuning Wang

Publication date: 26 January 2023

Published in: Numerical Algorithms (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2202.11229

zbMATH Keywords

optimal approximationfinite element exterior calculusgeneralized barycentric coordinatespolygonal meshesserendipity finite elementsdirect finite elements

Mathematics Subject Classification ID

Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Numerical interpolation (65D05) de Rham theory in global analysis (58A12) Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs (65N50)

Uses Software

• PolyMesher

Cites Work

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• \texttt{PolyMesher}: a general-purpose mesh generator for polygonal elements written in Matlab
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• Global Estimates for Mixed Methods for Second Order Elliptic Equations
• Quadratic serendipity finite elements on polygons using generalized barycentric coordinates
• Finite element exterior calculus: from Hodge theory to numerical stability
• Mixed and nonconforming finite element methods : implementation, postprocessing and error estimates
• Finite Element Methods for Navier-Stokes Equations
• Mixed and Hybrid Finite Element Methods
• Finite element differential forms on cubical meshes

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