01342nam a2200169 a 4500 20260901030406.0 250101s2020 xx o 000 0 eng d Hengguang Li A $C^0$ finite element method for the biharmonic problem with Navier boundary conditions in a polygonal domain arXiv 2020 text online resource 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. Open access — freely available to read. https://arxiv.org/pdf/2012.12374v1 Read the full paper (PDF) ERES 701 701 0 0 0 3 GEN MAIN MAIN SCICOMP 2026-09-01 0 YGE000962 2026-09-01 03:04:07 https://arxiv.org/pdf/2012.12374v1 2026-09-01 PAPER