A one-dimensional inverse problem in composite materials: Regularization and error estimates
نویسندگان
چکیده
منابع مشابه
A Nonhomogeneous Backward Heat Problem: Regularization and Error Estimates
We consider the problem of finding the initial temperature, from the final temperature, in the nonhomogeneous heat equation ut − uxx = f(x, t), (x, t) ∈ (0, π)× (0, T ), u(0, t) = u(π, t) = 0, (x, t) ∈ (0, π)× (0, T ). This problem is known as the backward heat problem and is severely ill-posed. Our goal is to present a simple and convenient regularization method, and sharp error estimates for ...
متن کاملA Cauchy Problem for Helmholtz Equation : Regularization and Error Estimates
In this paper, the Cauchy problem for the Helmholtz equation is investigated. It is known that such problem is severely ill-posed. We propose a new regularization method to solve it based on the solution given by the method of separation of variables. Error estimation and convergence analysis have been given. Finally, we present numerical results for several examples and show the effectiveness ...
متن کاملRegularization and Hölder Type Error Estimates for an Initial Inverse Heat Problem with Time-dependent Coefficient
This paper discusses the initial inverse heat problem (backward heat problem) with time-dependent coefficient. The problem is ill-posed in the sense that the solution (if it exists) does not depend continuously on the data. Two regularization solutions of the backward heat problem will be given by a modified quasi-boundary value method. The Hölder type error estimates between the regularization...
متن کاملEquivalent a posteriori error estimates for spectral element solutions of constrained optimal control problem in one dimension
In this paper, we study spectral element approximation for a constrained optimal control problem in one dimension. The equivalent a posteriori error estimators are derived for the control, the state and the adjoint state approximation. Such estimators can be used to construct adaptive spectral elements for the control problems.
متن کاملA regularization method for solving a nonlinear backward inverse heat conduction problem using discrete mollification method
The present essay scrutinizes the application of discrete mollification as a filtering procedure to solve a nonlinear backward inverse heat conduction problem in one dimensional space. These problems are seriously ill-posed. So, we combine discrete mollification and space marching method to address the ill-posedness of the proposed problem. Moreover, a proof of stability and<b...
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: Applied Mathematical Modelling
سال: 2015
ISSN: 0307-904X
DOI: 10.1016/j.apm.2015.01.004