REST와 Sp1에 의한 Brain specific homeobox 유전자의 전사조절에 관한 연구

Thesis(doctors) --서울대학교 대학원 :생명과학부,2008.2.Docto

An Analysis of the Simplest Mixed Finite Element Method for the Elastic Wave Equation

학위논문 (석사)-- 서울대학교 대학원 : 수리과학부, 2015. 2. 신동우.Although it is well-known that there are various mixed finite elements for solving elastic wave equation, in this paper, we will approach the elastic wave equation with 2D, the simplest mixed finite element method. The superiority of the family of elements over the existing elements is its simplicity and high accuracy. It satisfies the discrete inf-sup condition for the stability analysis and has convergence property of the consistency error. In this paper, by using this mixed finite element method, we will get the approximated solution of the elastic wave equation, and also prove that this approximated solution stably converges to real solution through elliptic projection.1 Introduction 1 2 Preliminaries 4 2.1 The model problem . . . . . . . . . . . . . . . . . . . . . . . . 4 2.2 A minimal element in 2D . . . . . . . . . . . . . . . . . . . . . 7 2.3 The elliptic problem . . . . . . . . . . . . . . . . . . . . . . . . 10 3 Analysis of the Elastic Wave Equation 13 3.1 Problem setting . . . . . . . . . . . . . . . . . . . . . . . . . . 13 3.2 Analysis of mixed finite element for an elliptic problem . . . . 14 3.3 Application to the elliptic projection operator . . . . . . . . . 21 3.4 Analysis of mixed finite element for an elastic wave equation . 22 4 Numerical Result 29 4.1 Numerical Result for elliptic problem . . . . . . . . . . . . . . 29 4.2 Numerical Result for elastic wave equation . . . . . . . . . . . 39 Abstract (in Korean)Maste