An Efficient Two-Grid High-order Compact Difference Scheme with Variable-Step BDF2 Method for Semilinear Parabolic Equations

主讲人：付红斐

摘要：Due to the lack of corresponding analysis on appropriate mapping operator between two grids, high-order two-grid difference algorithms are rarely studied. In this talk, we first construct a variable-step high-order nonlinear difference algorithm using compact difference technique in space and the second-order backward differentiation formula (BDF2) with variable temporal stepsize in time. With the help of discrete orthogonal convolution kernels and a cut-off numerical technique, the unique solvability and corresponding error estimates of the high-order nonlinear difference scheme are established. Then, an efficient two-grid high-order difference algorithm is developed by combining a small-scale variable-step high-order nonlinear difference algorithm on the coarse grid and a large-scale variable-step high-order linearized difference algorithm on the fine grid, in which the piecewise bi-cubic Lagrange interpolation mapping operator is adopted to project the coarse-grid solution to the fine grid. Under a weaker maximum temporal stepsize condition, optimal fourth-order in space and second-order in time error estimates of the two-grid difference scheme is established. Finally, several numerical experiments are carried out to demonstrate the effectiveness and efficiency of the proposed scheme..

主讲人简介：付红斐，中国海洋大学数学科学学院教授、博士生导师，兼任中国工业与应用数学学会油水资源数值方法专委会委员、山东数学会计算数学专委会委员等。主要从事偏微分方程数值解法、最优控制问题数值算法和分数阶微分方程数值理论和快速算法方面的研究和教学工作。近年来先后主持、参与国家自然科学基金（重点、面上、青年）、山东省自然科学基金（面上、青年）等，发表SCI论文60余篇。曾获山东省科学技术奖自然科学二等奖；2020年入选中国海洋大学“青年英才工程”第一层次人才计划。

邀请人：黄乘明

时间：12月8日16:00-18：00