Gradient-based estimation of uncertain parameters for elliptic partial differential equations

A Posteriori Error Estimation for Elliptic Partial Differential Equations

These lecture notes comprise the talks of the author on “A posteriori error estimates for modelling errors” and on “A posteriori error estimates for highly indefinite problems” given at the Zürich Summerschool 2012. 1 Lecture 1: Combined A Posteriori Modeling Discretization Error Estimate for Elliptic Problems with Complicated Interfaces Remark. This part of the lecture notes is a slightly exte...

global results on some nonlinear partial differential equations for direct and inverse problems

در این رساله به بررسی رفتار جواب های رده ای از معادلات دیفرانسیل با مشتقات جزیی در دامنه های کراندار می پردازیم . این معادلات به فرم نیم-خطی و غیر خطی برای مسایل مستقیم و معکوس مورد مطالعه قرار می گیرند . به ویژه، تاثیر شرایط مختلف فیزیکی را در مساله، نظیر وجود موانع و منابع، پراکندگی و چسبندگی در معادلات موج و گرما بررسی می کنیم و به دنبال شرایطی می گردیم که متضمن وجود سراسری یا عدم وجود سراسر...

Essential Spectra of Elliptic Partial Differential Equations

Let A be a closed, densely defined operator in a Banach space X. There are several definitions of the "essential" spectrum of A (cf. [ l ] , [2]). According to Wolf [3], [4] it is the complement in the complex plane of the $-set of A. The $-set $A of A is the set of points X for which (a) a(A — X), the dimension of the null space of A — X, is finite (b) R(A —X), the range of A —X, is closed (c)...

A Generalized Conjugate Gradient Method for the Numerical Solution of Elliptic Partial Differential Equations

We consider a generalized conjugate gradient method for solving sparse, symmetric, positive-definite systems of linear equations, principally those arising from the discretization of boundary value problems for elliptic partial differential equations. The method is based on splitting off from the original coefficient matrix a symmetric, positive-definiteonethat corresponds to a more easily solv...

Lecture Notes on Elliptic Partial Differential Equations