연세대학교 계산과학공학

Speaker: Prof. JaEun Ku (Oklahoma State University)

Date: 2023.10.24 / 1:30pm

Place:  ASTC 516 (첨단관 516호)

Talk Title: Dual finite element methods for singularly perturbed reaction-diffusion problems

Abstract

Recently, dual finite element methods are developed for accurate and efficient approximations of solutions of singularly perturbed reaction-diffusion problems.  

The methods only approximate the dual variables without approximating the primary variable.  An approximation for the primary variable can be recovered through a simple

local $L_2$ projection. The methods provide a competitive alternative to the other existing numerical methods.  For example, the approximation solution for the primary variable does not show numerical oscillation, which is observed in the standard Galerkin methods.  The first part of this talk introduces the dual finite element methods, and the second part presents various a priori and a posteriori error estimates including guaranteed upper bounds for dual approximation.