Exact Integration for singular Zienkiewicz and Guzman-Neilan Finite Elements with Implementation
Lars Diening, Johannes Storn, Tabea Tscherpel
TL;DR
This paper introduces a recursive integration method for rational polynomials in 2D and provides Matlab implementations of singular Zienkiewicz and Guzman-Neilan finite elements with rational basis functions.
Contribution
It develops a recursive integration formula and offers practical Matlab implementations for specific rational basis function finite elements.
Findings
Efficient recursive integration formula for rational polynomials.
Implementation of singular Zienkiewicz and Guzman-Neilan finite elements.
Facilitates practical use of rational basis function finite elements.
Abstract
We develop a recursive integration formula for a class of rational polynomials in 2D. Based on this, we present implementations of finite elements that have rational basis functions. Specifically, we provide simple Matlab implementations of the singular Zienkiewicz and the lowest-order Guzman-Neilan finite element in 2D.
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Taxonomy
TopicsDifferential Equations and Boundary Problems · Nonlinear Differential Equations Analysis · Holomorphic and Operator Theory