A new mixed finite-element method for H2 elliptic problems

Fourth-order differential equations play an important role in many applications science and engineering. In this paper, we present a three-field mixed finite-element formulation for fourth-order problems, with focus on the effective treatment of different boundary conditions that arise naturally variational formulation. Our is based introducing gradient solution as explicit variable, constrained using Lagrange multiplier. The essential are enforced weakly, Nitsche's method where required. As result, problem rewritten saddle-point system, requiring analysis resulting discretization construction optimal linear solvers. Here, discuss well-posedness accuracy Moreover, develop monolithic multigrid solvers systems. Two three-dimensional numerical results presented to demonstrate efficiency proposed.