A Morley Type Triangular Finite Element with High Convergence for the Biharmonic Problem

A Morley Type Triangular Finite Element with High Convergence for the Biharmonic Problem

In this work, we construct a theoretical framework to develop non <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>C</mi><mn>0</mn></msup></semantics></math><...

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Bibliographic Details
Main Authors: Yuan Bao, Sibo Yang
Format: Article
Language:English
Published: MDPI AG 2024-10-01
Series:Mathematics
Subjects:
biharmonic problem
Morley type element
high convergence
nonconforming element
Online Access:https://www.mdpi.com/2227-7390/12/20/3199
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Summary:In this work, we construct a theoretical framework to develop non <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>C</mi><mn>0</mn></msup></semantics></math></inline-formula> Morley type nonconforming high-convergence elements for biharmonic problems. For each element domain, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>P</mi><mn>3</mn></msub></semantics></math></inline-formula> should be included in the space of shape functions. Besides the degrees of freedom of Morley elements, we add the integrals and first-order moments of the normal derivatives on edges. The choice of degrees of freedom and shape function space guarantees the possibility of improving the convergence order. As an application, we specifically construct a Morley type element on triangular meshes. Lastly, numerical experiments are carried out to verify the feasibility of the element.
ISSN:2227-7390

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