讲座主题：Analysis of bound preserving time-implicit discretizations

专家姓名：闫凤娜

工作单位：合肥工业大学

讲座时间：2026年11月11日 09:00-10:00

讲座地点：腾讯会议：482-684-051

主办单位：烟台大学数学与信息科学学院

内容摘要：

We first develop entropy-dissipative, high-order local discontinuous Galerkin (LDG) discretizations coupled with diagonally implicit Runge–Kutta (DIRK) methods for nonlinear degenerate parabolic equations. To preserve positivity, we incorporate Karush–Kuhn–Tucker (KKT) conditions into the high-order DIRK–LDG discretizations through Lagrange multipliers. Under a suitable time–step restriction, we establish the unique solvability and entropy dissipation of the positivity-preserving LDG discretization that is first-order accurate in time and high-order accurate in space under periodic boundary conditions. To reduce the size of the nonlinear system arising from the direct enforcement of pointwise bounds, we further propose a two–stage limiting strategy for convection–diffusion–reaction equations. The KKT limiter is first used to enforce the prescribed bounds on cell averages, after which an explicit bound–preserving limiter imposes the corresponding pointwise bounds. We prove the unique solvability of the resulting average bound-preserving backward differentiation formula (BDF)–LDG discretizations and establish stability and optimal error estimates for BDF2–LDG scheme. Numerical results are presented to validate the accuracy and effectiveness of the proposed method in preserving the bounds.

主讲人介绍：

闫凤娜，中国科学技术大学和荷兰特文特大学博士，现任在合肥工业大学讲师。主要研究非线性偏微分方程高阶保界数值格式的构造与分析，目前已发表13篇SCI论文，主持国家自然科学基金青年项目和安徽省自然科学基金青年项目。