Hypercircle estimates for nonlinear problems

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...

A posteriori estimators for obstacle problems by the hypercircle method

A posteriori error estimates for the obstacle problem are established in the framework of the hypercircle method. To this end, we provide a general theorem of Prager– Synge type. There is now no generic constant in the main term of the estimate. Moreover, the role of edge terms is elucidated, and the analysis also applies to other types of a posteriori error estimators for obstacle problems.

Finite element error estimates for nonlinear convective problems

A posteriori error estimates for nonlinear problems. Lr-estimates for finite element discretizations of elliptic equations

— We extend the gênerai framework of [18] for deriving a posteriori error estimâtes for approximate solutions of noniinear elliptic problems such ihat it also yields L'-error estimâtes. The gênerai results are applied to finite element discretizations of scalar quasilinear elliptic pdes of 2nd order and the stationary incompressible Navier-Stokes équations. They immediately yield a posteriori e...

A numerical scheme for solving nonlinear backward parabolic problems

‎In this paper a nonlinear backward parabolic problem in one‎ ‎dimensional space is considered‎. ‎Using a suitable iterative‎ ‎algorithm‎, ‎the problem is converted to a linear backward parabolic‎ ‎problem‎. ‎For the corresponding problem‎, ‎the backward finite‎ ‎differences method with suitable grid size is applied‎. ‎It is shown‎ ‎that if the coefficients satisfy some special conditions‎, ‎th...