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Title: On Integral Equation Methods for the First Dirichlet Problem of the Biharmonic and Modified Biharmonic Equations in NonSmooth Domains
Award ID(s):
1720405
NSF-PAR ID:
10100021
Author(s) / Creator(s):
;
Date Published:
Journal Name:
SIAM Journal on Scientific Computing
Volume:
40
Issue:
4
ISSN:
1064-8275
Page Range / eLocation ID:
A2609 to A2630
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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  1. Abstract In this paper we study the biharmonic equation with Navier boundary conditions in a polygonal domain. In particular, we propose a method that effectively decouples the fourth-order problem as a system of Poisson equations. Our method differs from the naive mixed method that leads to two Poisson problems but only applies to convex domains; our decomposition involves a third Poisson equation to confine the solution in the correct function space, and therefore can be used in both convex and nonconvex domains. A $C^0$ finite element algorithm is in turn proposed to solve the resulting system. In addition, we derive 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. 
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