A $C^0$ finite element method for the biharmonic problem with Navier boundary conditions in a polygonal domain (Record no. 701)

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fixed length control field 01342nam a2200169 a 4500
005 - DATE AND TIME OF LATEST TRANSACTION
control field 20260901030406.0
008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION
fixed length control field 250101s2020 xx o 000 0 eng d
100 1# - MAIN ENTRY--PERSONAL NAME
Personal name Hengguang Li
245 10 - TITLE STATEMENT
Title A $C^0$ finite element method for the biharmonic problem with Navier boundary conditions in a polygonal domain
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Name of producer, publisher, distributor, manufacturer arXiv
Date of production, publication, distribution, manufacture, or copyright notice 2020
336 ## - CONTENT TYPE
Content type term text
338 ## - CARRIER TYPE
Carrier type term online resource
520 ## - SUMMARY, ETC.
Summary, etc. In this paper, we study the biharmonic equation with the Navier boundary conditions in a polygonal domain. In particular, we propose a method that effectively decouples the 4th-order problem into a system of Poisson equations. Different from the usual mixed method that leads to two Poisson problems but only applies to convex domains, the proposed decomposition involves a third Poisson equation to confine the solution in the correct function space, and therefore can be used in both convex and non-convex domains. A $C^0$ finite element algorithm is in turn proposed to solve the resulted system. In addition, we derive the optimal error estimates for the numerical solution on both quasi-uniform meshes and graded meshes. Numerical test results are presented to justify the theoretical findings.
506 0# - RESTRICTIONS ON ACCESS NOTE
Terms governing access Open access — freely available to read.
856 40 - ELECTRONIC LOCATION AND ACCESS
Uniform Resource Identifier <a href="https://arxiv.org/pdf/2012.12374v1">https://arxiv.org/pdf/2012.12374v1</a>
Link text Read the full paper (PDF)
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      Available online General Yegates University Library Yegates University Library Science and Computing 09/01/2026   YGE000962 09/01/2026 https://arxiv.org/pdf/2012.12374v1 09/01/2026 Research paper — read online