C0 IP Methods for the Transmission Eigenvalue Problem
نویسندگان
چکیده
We consider a non-self-adjoint fourth order eigenvalue problem using a discontinuous Galerkin (DG) method. For high order problems, DG methods are competitive since they use simple basis functions and have less degrees of freedom. The numerical implementation is much easier compared with classical finite element methods. In this paper, we propose an interior penalty discontinuous Galerkin method using C Lagrange elements (CIPG) for the transmission eigenvalue problem and prove the optimal convergence. The method is applied to various examples and its effectiveness is validated.
منابع مشابه
A C linear finite element method for two fourth-order eigenvalue problems
In this article, we construct aC0 linear finite element method for two fourth-order eigenvalue problems: the biharmonic and the transmission eigenvalue problems. The basic idea of our construction is to use gradient recovery operator to compute the higher-order derivatives of a C0 piecewise linear function, which do not exist in the classical sense. For the biharmonic eigenvalue problem, the op...
متن کاملOn the nonnegative inverse eigenvalue problem of traditional matrices
In this paper, at first for a given set of real or complex numbers $sigma$ with nonnegative summation, we introduce some special conditions that with them there is no nonnegative tridiagonal matrix in which $sigma$ is its spectrum. In continue we present some conditions for existence such nonnegative tridiagonal matrices.
متن کاملLooking for the Best Constant in a Sobolev Inequality: A Numerical Approach
A numerical method for the computation of the best constant in a Sobolev inequality involving the spacesH2(Ω) and C0(Ω) is presented. Green’s functions corresponding to the solution of Poisson problems are used to express the solution. This (kind of) non-smooth eigenvalue problem is then formulated as a constrained optimization problem and solved with two different strategies: an augmented Lagr...
متن کاملEvolution of the first eigenvalue of buckling problem on Riemannian manifold under Ricci flow
Among the eigenvalue problems of the Laplacian, the biharmonic operator eigenvalue problems are interesting projects because these problems root in physics and geometric analysis. The buckling problem is one of the most important problems in physics, and many studies have been done by the researchers about the solution and the estimate of its eigenvalue. In this paper, first, we obtain the evol...
متن کاملAn Interior Penalty Method with C Finite Elements for the Approximation of the Maxwell Equations in Heterogeneous Media: Convergence Analysis with Minimal Regularity
The present paper proposes and analyzes an interior penalty technique using C0-finite elements to solve the Maxwell equations in domains with heterogeneous properties. The convergence analysis for the boundary value problem and the eigenvalue problem is done assuming only minimal regularity in Lipschitz domains. The method is shown to converge for any polynomial degrees and to be spectrally cor...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- J. Sci. Comput.
دوره 68 شماره
صفحات -
تاریخ انتشار 2016