A review on arbitrarily regular conforming virtual element methods for second- and higher-order elliptic partial differential equations

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...

Conforming and Nonconforming Virtual Element Methods for Elliptic Problems

We present, in a unified framework, new conforming and nonconforming Virtual Element Methods (VEM) for general second order elliptic problems in two and three dimensions. The differential operator is split into its symmetric and non-symmetric parts and conditions for stability and accuracy on their discrete counterparts are established. These conditions are shown to lead to optimal H1and L2-err...

Finite element methods for semilinear elliptic stochastic partial differential equations

We study finite element methods for semilinear stochastic partial differential equations. Error estimates are established. Numerical examples are also presented to examine our theoretical results. Mathematics Subject Classification (2000) 65N30 · 65N15 · 65C30 · 60H15

Variational Approximation of Flux in Conforming Finite Element Methods for Elliptic Partial Differential Equations: a Model Problem

A Higher Order Finite Element Method for Partial Differential Equations on Surfaces

A new higher order finite element method for elliptic partial differential equations on a stationary smooth surface Γ is introduced and analyzed. We assume Γ is characterized as the zero level of a level set function φ and only a finite element approximation φh (of degree k ≥ 1) of φ is known. For the discretization of the partial differential equation, finite elements (of degree m ≥ 1) on a pi...