報告題目：Discontinuous Galerkin method with Lagrange multiplier (DGLM) for elliptic problem
報告人：Mi-Young Kim 韓國仁荷大學
時間：2024年 08月29日（星期四）9:55-10:40
地點: 正新樓209
校内聯系人：王瑞姝 wangrs_math@jlu.edu.cn
報告摘要：Arbitrary high order discontinuous Galerkin methods with Lagrange multiplier (DGLM) are developed for elliptic and convection-diffusion-reaction equations. Lagrange multiplier is introduced on the edge/face of each element through the definition of a weak divergence and a weak derivative. A local weak formulation is derived by weakly imposing Dirichlet boundary condition with Lagrange multiplier on the edges/faces. The global weak formulation is given as the sum of the local problems. Stability of the method and the error estimates are derived in a broken norm. An edgewise iterative scheme for the DGLM solution is
also developed. Convergence analysis of the scheme is given. Efficiency of the iterative scheme is tested for the elliptic problem with adaptive mesh refinement. Several numerical examples are presented.
報告人簡介：Mi-Young Kim 是韓國仁荷大學教授。主要的研究方向有數學生物學，非線性波，數值天氣預報，不連續Galerkin有限元法，區域分解法，多尺度方法等。在 SIAM J. Numer. Anal., SIAM J. Sci. Comp., Comput. Methods Appl. Mech. Engrg.等期刊發表論文50餘篇。
