Condition Number Estimates for C Interior Penalty Methods
نویسندگان
چکیده
where f ∈ L2(Ω). Let Th be a simplicial or convex quadrilateral triangulation of Ω. In C 0 interior penalty methods, we choose the discrete space Vh ⊂ H 1 0 (Ω) to be either a P` (` ≥ 2) triangular Lagrange finite element space or a Q` (` ≥ 2) tensor product finite element space associated with Th. By an integration by parts argument [4], it can be shown that the solution u of (1), which belongs to H(Ω) for some α > 1/2 by elliptic regularity [11, 9, 13, 2], satisfies
منابع مشابه
Interior Penalty Discontinuous Approximations of Elliptic Problems
This paper studies an interior penalty discontinuous approximation of elliptic problems on non–matching grids. Error analysis, interface domain decomposition type preconditioners, as well as numerical results illustrating both, discretization errors and condition number estimates of the problem and reduced forms of it, are presented.
متن کاملUN CO RR EC TE D PR O O F 1 A Two - Level Additive Schwarz Preconditioner for C 0 2 Interior Penalty Methods for Cahn - Hilliard Equations 3
We study a two-level additive Schwarz preconditioner for C0 interior penalty 7 methods for a biharmonic problem with essential and natural boundary conditions with Cahn8 Hilliard type. We show that the condition number of the preconditioned system is bounded 9 by C(1+(H3/δ 3)), where H is the typical diameter of a subdomain, δ measures the overlap 10 among the subdomains, and the positive const...
متن کاملA Nonoverlapping Domain Decomposition Preconditioner for a Symmetric Interior Penalty Method
In this talk we will discuss a nonoverlapping domain decomposition pre-conditioner for the symmetric interior penalty Galerkin method [1, 2, 3]. Thepreconditioner is based on balancing domain decomposition by constraints [4].Theoretical results on the condition number estimate of the preconditioned sys-tem will be presented along with numerical results. References[1] J. ...
متن کاملAn A Posteriori Analysis of C0 Interior Penalty Methods for the Obstacle Problem of Clamped Kirchhoff Plates
We develop an a posteriori analysis of C interior penalty methods for the displacement obstacle problem of clamped Kirchhoff plates. We show that a residual based error estimator originally designed for C interior penalty methods for the boundary value problem of clamped Kirchhoff plates can also be used for the obstacle problem. We obtain reliability and efficiency estimates for the error esti...
متن کاملA BDDC Preconditioner for a Weakly Over-Penalized Symmetric Interior Penalty Method
ABSTRACT In this talk we will discuss a nonoverlapping domain decomposition preconditioner for the weakly over-penalized symmetric interior penalty (WOPSIP) method. The WOPSIP method belongs to the family of discontinuous finite element methods. The preconditioner for the WOPSIP method is based on the balancing domain decomposition by constraints methodology. Theoretical results on the conditio...
متن کامل