Convergence of free boundaries in discrete obstacle problems
نویسنده
چکیده
We show that a piecewise linear finite element approximation of the obstacle problem gives an approximate free boundary converges, in an appropriate distance, to the free boundary of the continuous problemunder a stability condition on the obstacle.
منابع مشابه
Homogenization of a Hele-Shaw problem in periodic and random media
We investigate the homogenization limit of a free boundary problem with space-dependent free boundary velocities. The problem under consideration has a well-known obstacle problem transformation, formally obtained by integrating with respect to the time variable. By making rigorous the link between these two problems, we are able to derive an explicit formula for the homogenized free boundary v...
متن کاملHomogenization of a Hele-Shaw type problem in periodic and random media
We investigate the homogenization limit of a free boundary problem with space-dependent free boundary velocities. The problem under consideration has a well-known obstacle problem transformation, formally obtained by integrating with respect to the time variable. By making rigorous the link between these two problems, we are able to derive an explicit formula for the homogenized free boundary v...
متن کاملA direct algorithm in some free boundary problems
In this paper we propose a new algorithm for the well known elliptic obstacle problem and for parabolic variational inequalities like oneand two-phase Stefan problem and of obstacle type. Our approach enters the category of xed domain methods and solves just linear elliptic or parabolic equations and their discretization at each iteration. We prove stability and convergence properties. The appr...
متن کاملA Monotonic Method for the Numerical Solution of Some Free Boundary Value Problems
This work presents an efficient monotonic algorithm for the numerical solution of the obstacle problem and the Signorini problems, when they are discretized either by the finite element method or by the finite volume method. The convergence of this algorithm applied to the discrete problem is proven in both cases.
متن کاملMoving Mesh Finite Element Approximations for Variational Inequality I: Static Obstacle Problem
Finite element schemes loose accuracy when approximating a class of vari-ational inequalities, elliptic obstacle problems, due to the existence of free boundaries. In this paper, moving mesh nite element method is applied to solve the elliptic obstacle problems. Computational meshes are constructed by combining harmonic mapping and sharper a posteriori error estimators which are normally used i...
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:
- Numerische Mathematik
دوره 106 شماره
صفحات -
تاریخ انتشار 2007