Unified a priori analysis of four second-order FEM for fourth-order quadratic semilinear problems (Q6135911)

In this paper, a unified framework is considered for fourth-order semilinear elliptic problems with trilinear nonlinearity and with a source term in a bounded polygonal Lipschitz domain, which allows for quasi-best approximation with lowest-order finite element methods. This applies simultaneously to the Morley finite element method, the discontinuous Galerkin, the \(C_0\) interior penalty and the weakly over-penalized symmetric interior penalty scheme for the approximation of a regular solution to a fourth-order semilinear problem with the biharmonic operator as the leading term. The results are verified for the 2D Navier-Stokes equations in the stream function vorticity formulation and for the von Kármán equations.