Optimal order error estimates for finite element approximations of a bifurcation function
نویسندگان
چکیده
منابع مشابه
Some Optimal Error Estimates for Piecewise Linear Finite Element Approximations
It is shown that the Ritz projection onto spaces of piecewise linear finite elements is bounded in the Sobolev space, Wp\ for 2 <p < oo. This implies that for functions in W¿ n Wp the error in approximation behaves like 0(h) in Wx, for 2 <p =c oo, and like 0(h2) in Lp, for 2 *íp < oo. In all these cases the additional logarithmic factor previously included in error estimates for linear finite e...
متن کاملError Estimates of Mixed Finite Element Approximations for a Class of Fourth Order Elliptic Control Problems
In this paper, we consider the error estimates of the numerical solutions of a class of fourth order linear-quadratic elliptic optimal control problems by using mixed finite element methods. The state and co-state are approximated by the order k Raviart-Thomas mixed finite element spaces and the control variable is approximated by piecewise polynomials of order k (k ≥ 1). L and L-error estimate...
متن کاملError Estimates for Finite Element Approximations of Elliptic Control Problems
We investigate finite element approximations of one-dimensional elliptic control problems. For semidiscretizations and full discretizations with piecewise constant controls we derive error estimates in the maximum norm.
متن کاملA Posteriori Error Estimates for Mixed Finite Element Galerkin Approximations to Second Order Linear Hyperbolic Equations
In this article, a posteriori error analysis for mixed finite element Galerkin approximations of second order linear hyperbolic equations is discussed. Based on mixed elliptic reconstructions and an integration tool, which is a variation of Baker’s technique introduced earlier by G. Baker (SIAM J. Numer. Anal., 13 (1976), 564-576) in the context of a priori estimates for a second order wave equ...
متن کاملQuasi - Optimal Estimates for Finite Element Approximations Using Orlicz Norms
We consider the approximation by linear finite elements of the solution of the Dirichlet problem -Au = /. We obtain a relation between the error in the infinite norm and the error in some Orlicz spaces. As a consequence, we get quasi-optimal uniform estimates when u has second derivatives in the Orlicz space associated with the exponential function. This estimate contains, in particular, the ca...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Computational and Applied Mathematics
سال: 2005
ISSN: 0377-0427
DOI: 10.1016/j.cam.2004.11.034