Solution of Nonlinear Elliptic Boundary Value Problems and Its Iterative Construction
نویسندگان
چکیده
منابع مشابه
Solution of Nonlinear Elliptic Boundary Value Problems and Its Iterative Construction
and Applied Analysis 3 2. Preliminaries Now, we list some of the knowledge we need in the sequel. Let X be a real Banach space with a strictly convex dual space X∗. We use ·, · to denote the generalized duality pairing between X and X∗. We use “→ ” to denote strong convergence. Let “X ↪→ Y” denote the space X embedded continuously in space Y . For any subset G of X, we denote by intG its interi...
متن کاملNonlinear Elliptic Boundary Value Problems
It is the object of the present note to present a new nonlinear version of the orthogonal projection method for proving the existence of solutions of nonlinear elliptic boundary value problems. The key point in this method is the application of a new general theorem concerning the solvability of nonlinear functional equations in a reflexive Banach space involving operators which may not be cont...
متن کاملParallel Solution of Elliptic Boundary Value Problems
We describe the development of some parallel iterative techniques for solving boundary value problems for elliptic partial differential equations. Using domain decomposition techniques, we modify standard sequential iterative techniques to obtain effective parallel methods. We contrast implementations on distributed-memory and shared-memory scalable parallel processors. We describe the use of t...
متن کاملIterative Schemes for Nonsymmetric and Indefinite Elliptic Boundary Value Problems
The purpose of this paper is twofold. The first is to describe some simple and robust iterative schemes for nonsymmetric and indefinite elliptic boundary value problems. The schemes are based in the Sobolev space Hl (ii) and require minimal hypotheses. The second is to develop algorithms utilizing a coarse-grid approximation. This leads to iteration matrices whose eigenvalues lie in the right h...
متن کاملElliptic Boundary-Value Problems
In the first part of this chapter we focus on the question of well-posedness of boundary-value problems for linear partial differential equations of elliptic type. The second part is devoted to the construction and the error analysis of finite difference schemes for these problems. It will be assumed throughout that the coefficients in the equation, the boundary data and the resulting solution ...
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: Abstract and Applied Analysis
سال: 2012
ISSN: 1085-3375,1687-0409
DOI: 10.1155/2012/210325