Quadrature finite element method for elliptic eigenvalue problems
The author considers a positive semi-definite eigenvalue problem for second-order self-adjoint elliptic differential operators with Dirichlet boundary conditions which is posed on a bounded domain in two dimensions with smooth boundary. The stated problem has a nondecreasing sequence of positive eigenvalues of finite multiplicity with a limit point at infinity. To the sequence of eigenvalues, there corresponds an orthonormal system of eigenfunctions. A finite element method with numerical integration and Lagrange curved triangular finite elements of arbitrary order is applied. Error estimates for approximate eigenvalues and eigenfunctions are proved.
second-order self-adjoint elliptic differential operator
scientific article; zbMATH DE number 6815761
scientific article