A priori and a posteriori error estimates are derived for the numerical approximation of scalar and complex valued phase field models. Particular attention is devoted to the dependence of the estimates on a small parameter. For typical singularities the estimates depend on the inverse of the parameter in a polynomial as opposed to exponential dependence of estimates resulting from a straightfor...

Optimal a posteriori error estimates in L∞(0, T ; L(Ω)) are derived for the finite element approximation of Allen-Cahn equations. The estimates depend on the inverse of a small parameter only in a low order polynomial and are valid past topological changes of the evolving interface. The error analysis employs an elliptic reconstruction of the approximate solution and applies to a large class of...

Quasi-optimal a posteriori error estimates in L∞(0, T ;L2(Ω)) are derived for the finite element approximation of Allen-Cahn equations. The estimates depend on the inverse of a small parameter only in a low order polynomial and are valid past topological changes of the evolving interface. The error analysis employs an elliptic reconstruction of the approximate solution and applies to a large cl...

Given data drawn from a mixture of multivariate Gaussians, a basic problem is to accurately estimate the mixture parameters. We provide a polynomial-time algorithm for this problem for the case of two Gaussians in n dimensions (even if they overlap), with provably minimal assumptions on the Gaussians, and polynomial data requirements. In statistical terms, our estimator converges at an inverse ...

This paper reports on application of theory of experimental design using graphical techniques in R programming language and application of nonlinear bootstrap regression method to demonstrate the invariant property of parameter estimates of the Inverse polynomial Model IPM in a nonlinear surface.

A solution of linear operator equations in the Hilbert space is constructed by using the best polynomial approximation of the inverse operator. This approach gives rise to certain iteration processes. Error estimates manifest that the suggested schemes may be fairly efficient. c © 2006 Elsevier Ltd. All rights reserved.

We present a general approach to obtain direct and inverse results for approximation in Hölder norms. This approach is used to obtain a collection of new results related with estimates of the best polynomial approximation and with the approximation by linear operators of non-periodic functions in Hölder norms. © 2005 Elsevier Inc. All rights reserved.

My general research areas are sensitivity analysis and computational error estimation for numerical solutions of differential equations. Most of my research focuses on inverse problems with the specific goal of quantifying the uncertainty of input parameters given uncertain output data. I obtained my thesis at Colorado State University under the supervision of Dr. Don Estep where we developed a...

in this research, the spatial distribution of electrical conductivity and ph of springs, ghanats and the base flow concentration places on the streams of central and south-west and central parts of the hamedan-bahar plain were evaluated. using different geostatistical methods such as kriging, minimum curvature, inverse distance, natural neighbor, local polynomial and radial basis functions, 108...