Legendre-Galerkin spectral-element method for the biharmonic equations and its applications (Q1672655)

The authors analyze the convergence of a Legendre-Galerkin spectral-element method applied to a two-dimensional biharmonic equation posed on a square. By constructing appropriate basis functions which satisfy the boundary conditions of the differential equations, the discrete variational formulation is reduced to a linear system with sparse and symmetric matrices, which can be solved using a Schur-complement method. Some error estimates are derived. The proposed method is applied to calculate the displacement of an elastic plate under a uniform applied load and stream function of zero Reynolds number flow in a driven cavity.