Spectral Element Method for Mixed Inhomogeneous Boundary Value Problems of Fourth Order

Abstract

In this paper, we investigate spectral element method for fourth order problems with mixed inhomogeneous boundary conditions. Some results on the composite Legendre quasi-orthogonal approximation are established, which play important roles in spectral element method with non-uniform meshes and non-uniform approximation modes. As an example of applications, the spectral element scheme is provided for a model problem, with the convergence analysis. Numerical results demonstrate its spectral accuracy, and coincide with the analysis well. In particular, the suggested method is convenient for local mesh refinement and local mode increment, and so it works well even for the solutions changing rapidly, oscillating seriously, or behaving differently in different subdomains.