Hp Local Discontinuous Galerkin Finite Element Method Based on Steklov Eigenvalue Problem

The flexibility and applicability of the finite element method can be used to solve the problem of the solution of elements with different shapes and properties. When there are very complex factors, such as uneven material properties, arbitrary boundary conditions, complex geometric shapes, etc., the finite element method can be flexibly processed and solved. The local discontinuous Galerkin method is used to solve the Steklov eigenvalue problem, in which the discontinuous Galerkin method can effectively solve the eigenvalue error problem. We propose a complete error estimation, and the hp prior error estimation can analyze the two-dimensional unstructured mesh with suspended nodes. The resulting mesh size h is optimal, and the degree p of the polynomial is suboptimal.