A <i>C</i>0 finite element method for the biharmonic problem with Navier boundary conditions in a polygonal domain

Abstract In this paper we study the biharmonic equation with Navier boundary conditions in a polygonal domain. particular, propose method that effectively decouples fourth-order problem as system of Poisson equations. Our differs from naive mixed leads to two problems but only applies convex domains; our decomposition involves third confine solution correct function space, and therefore can be used both nonconvex domains. A $C^0$ finite element algorithm is turn proposed solve resulting system. addition, derive optimal error estimates for numerical on quasi-uniform meshes graded meshes. Numerical test results are presented justify theoretical findings.