Approximation methods for nonlinear operator equations
نویسندگان
چکیده
منابع مشابه
External approximation of nonlinear operator equations
Based upon an external approximation scheme for the underlying Banach space, a nonlinear operator equation is approximated by a sequence of coercive problems. The equation is supposed to be governed by the sum of two nonlinear operators acting between a reflexive Banach space and its dual. Under suitable stability assumptions and if the underlying operators can be approximated consistently, wea...
متن کاملNonlinear Approximation and Adaptive Techniques for Solving Elliptic Operator Equations Multiscale Wavelet Methods for Pdes
w I n t r o d u c t i o n Adaptive methods are an important tool for numerically solving elliptic equations. Their origins appear in the adaptive grid refinements in finite element methods. Heuristically, adaptive methods are effective when trying to recover solutions u which exhibit singularities. Much impetus to the theory of adaptive finite element methods was provided by the introduction M ...
متن کاملNonlinear Approximation and Adaptive Techniques for Solving Elliptic Operator Equations
This survey article is concerned with two basic approximation concepts and their interrelation with the numerical solution of elliptic operator equations, namely nonlinear and adaptive approximation. On one hand, for nonlinear approximation based on wavelet expansions the best possible approximation rate, which a function can have for a given number of degrees of freedom, is characterized in te...
متن کاملAdaptive Wavelet Methods for Elliptic Operator Equations with Nonlinear Terms
We present an adaptive wavelet method for the numerical solution of elliptic operator equations with nonlinear terms. This method is developed based on tree approximations for the solution of the equations and adaptive fast reconstruction of nonlinear functionals of wavelet expansions. We introduce a constructive greedy scheme for the construction of such tree approximations. Adaptive strategie...
متن کاملOperator-splitting methods in respect of eigenvalue problems for nonlinear equations and applications for Burgers equations
In this article we consider iterative operator-splitting methods for nonlinear differential equations with respect to their eigenvalues. The main feature of the proposed idea is the fixed-point iterative scheme that linearizes our underlying equations. Based on the approximated eigenvalues of such linearized systems we choose the order of the the operators for our iterative splitting scheme. Th...
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: Proceedings of the American Mathematical Society
سال: 2002
ISSN: 0002-9939,1088-6826
DOI: 10.1090/s0002-9939-02-06769-2