01497nam a2200181 a 450000500170000000800400001710000170005724501150007426400160018933600090020533800200021452008040023450600460103885600660108494200090115099900130115995201430117220260901030406.0250101s2020    xx     o     000 0 eng d1 aHengguang Li10aA $C^0$ finite element method for the biharmonic problem with Navier boundary conditions in a polygonal domain 1barXivc2020  atext  aonline resource  aIn 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.0 aOpen access — freely available to read.40uhttps://arxiv.org/pdf/2012.12374v1yRead the full paper (PDF)  cERES  c701d701  001040738GENaMAINbMAINcSCICOMPd2026-09-01l0pYGE000962r2026-09-01 03:04:07uhttps://arxiv.org/pdf/2012.12374v1w2026-09-01yPAPER