講座主題：Stability and Superconvergence of MAC Scheme for Stokes Equations on Non-uniform Grids
專(zhuān)家姓名：芮洪興
工作單位：山東大學(xué)
講座時(shí)間：2017年8月31日（周四）下午16:00
講座地點(diǎn)：數(shù)學(xué)院大會(huì)議室
主辦單位：煙臺(tái)大學(xué)數(shù)學(xué)與信息科學(xué)學(xué)院
內(nèi)容摘要：
The marker and cell (MAC) method, a finite volume method based on staggered grids, has been one of the simplest and most effective numerical schemes for solving the Stokes and Navier-Stokes equations. Its superconvergence on uniform grids has been observed since 1992 but numerical analysis was not obtained completely. In this paper we establish the LBB condition and the stability for both velocity and pressure for MAC scheme of Stokes equations on non-uniform grids. Then we construct a auxiliary function depending on the velocity and discretizing parameters and analyze the superconvengence by using this function. We obtain the second order superconvergence in L2 norm for both velocity and pressure for the MAC scheme. We also obtain the second order superconvergence for some terms of H1 norm of the velocity, and the other terms of H1 norm are second order superconvergence on uniform grids. Numerical experiments using the MAC scheme show agreement of the numerical results with theoretical analysis.
主講人介紹：
山東大學(xué)教授，理學(xué)博士，博士生導(dǎo)師，山東大學(xué)數(shù)學(xué)學(xué)院副院長(zhǎng)。主要從事計(jì)算數(shù)學(xué)和應(yīng)用數(shù)學(xué)研究，包括有限元和混合元方法，有限體積元，差分算法，特征線算法等偏微分方程數(shù)值解法，流體及滲流力學(xué)問(wèn)題數(shù)值模擬方法及應(yīng)用軟件。發(fā)表論文140余篇，其中 SCI收錄近百余篇。現(xiàn)任中國(guó)工業(yè)與應(yīng)用數(shù)學(xué)學(xué)會(huì)常務(wù)理事、中國(guó)計(jì)算物理學(xué)會(huì)常務(wù)理事，曾任中國(guó)計(jì)算數(shù)學(xué)學(xué)會(huì)常務(wù)理事。
