Using finite element tools in proving shift theorems for elliptic boundary value problems
نویسندگان
چکیده
We consider the Laplace equation under mixed boundary conditions on a polygonal domain Ω. Regularity estimates in terms of Sobolev norms of fractional order for this type of problem are proved. The analysis is based on new interpolation results and multilevel representation of norms on the Sobolev spaces Hα(Ω). The Fourier transform and the construction of extension operators to Sobolev spaces on R are avoided in the proofs of the interpolation theorems.
منابع مشابه
B-Spline Finite Element Method for Solving Linear System of Second-Order Boundary Value Problems
In this paper, we solve a linear system of second-order boundary value problems by using the quadratic B-spline nite el- ement method (FEM). The performance of the method is tested on one model problem. Comparisons are made with both the analyti- cal solution and some recent results.The obtained numerical results show that the method is ecient.
متن کاملPreconditioning for Heterogeneous Problems
The main focus of this paper is to suggest a domain decomposition method for mixed finite element approximations of elliptic problems with anisotropic coefficients in domains. The theorems on traces of functions from Sobolev spaces play an important role in studying boundary value problems of partial differential equations. These theorems are commonly used for a priori estimates of the stabilit...
متن کاملError Estimates for the Finite Volume Element Method for Elliptic Pde’s in Nonconvex Polygonal Domains
We consider standard finite volume piecewise linear approximations for second order elliptic boundary value problems on a nonconvex polygonal domain. Based on sharp shift estimates, we derive error estimations in H –, L2– and L∞–norm, taking into consideration the regularity of the data. Numerical experiments and counterexamples illustrate the theoretical results.
متن کاملAdaptive Multilevel Techniques for Mixed Finite Element Discretizations of Elliptic Boundary Value Problems Technische Universit at M Unchen Cataloging Data : Adaptive Multilevel Techniques for Mixed Finite Element Discretizations of Elliptic Boundary Value Problems
We consider mixed nite element discretizations of linear second order elliptic boundary value problems with respect to an adaptively generated hierarchy of possibly highly nonuniform simplicial triangula-tions. By a well known postprocessing technique the discrete problem is equivalent to a modiied nonconforming discretization which is solved by preconditioned cg-iterations using a multilevel B...
متن کاملPotential theory for initial-boundary value problems of unsteady Stokes flow in two dimensions
Integral equations have been of great theoretical importance for analyzing boundary value problems. There is a large amount of literature devoted to the classical potential theory and its applications on solving the boundary value problems of elliptic partial differential equations (see, for example, [5, 20, 23, 25, 26, 31, 32, 36, 37, 40]). For elliptic problems, integral equations have been c...
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:
- Numerical Lin. Alg. with Applic.
دوره 10 شماره
صفحات -
تاریخ انتشار 2003