报告人：张强教授（南京大学）

报告题目：A local error estimate for Runge-Kutta discontinuous Galerkin methods applied to 2d linear hyperbolic equations with discontinuous initial data

报告摘要：In this talk we present a local error estimate for the Runge-Kutta discontinuous Galerkin methods applied to two-dimensional linear hyperbolic equations, in the case where the initial data is compactly supported and discontinuous along a straight line. Under suitable temporal-spatial conditions that ensure the L2-norm stability of this scheme, we obtain the optimal convergence order outside a narrow pollution region around the discontinuity, and we show that the pollution-region width is nearly optimal, being of onehalf order of the mesh size. The above result is achieved through a weighted energy analysis with a carefully-designed weight function. In this talk, we first present a uniform framework to establish the weighted L2-norm stability and successfully address the analysis difficulties for low-degree polynomials. Then we set up the weighted estimates related to the generalized Gauss-Radau projection and overcome the difficulties caused by multiple dimensions. Finally, numerical experiments are presented to verify our theoretical results.

报告时间：2026年11月15日9:00-10:00

报告地点：理学楼609室

报告人简介：张强，南京大学数学学院教授。南开大学数学系本硕博，中国科学技术大学博士后。长期从事偏微分方程数值方法研究，主攻间断有限元全离散格式的理论分析与应用，主持及参与多项国家基金项目，发表学术论文 60 余篇。

报告人：卢键方副教授（华南理工大学）

报告题目：An entropy stable oscillation-free discontinuous Galerkin method for hyperbolic conservation laws

报告摘要：In this talk, we introduce an innovative entropy-stable, oscillation-free discontinuous Galerkin (OFDG) scheme, referred to as ESOFDG, for the hyperbolic conservation laws. Entropy inequalities are crucial to the well-posedness of hyperbolic conservation laws, which help to select the physically meaningful one among the infinite many weak solutions. We extend the damping technique to the entropy stable quadrature-based DG methods. The newly added damping is independent of the given entropy pair and has entropy dissipation without comprising high order accuracy in the smooth region. Then entropy stability is obtained by using the convexity of the entropy functions and taking only one part of the local projections. By a careful theoretical analysis, the proposed algorithm still maintains the properties of the standard entropy stable quadrature-based DG methods. Several numerical experiments are presented to validate the theoretical findings and the capability of controlling spurious oscillations of the proposed algorithm.

报告时间：2026年11月15日10:00-11:00

报告地点：理学楼609室

报告人简介：卢键方，华南理工大学数学学院副教授，于2006年至2016年在中国科学技术大学获得理学学士学位和博士学位，2016至2018年在北京计算科学研究中心做博士后，2018年至2021年在华南师范大学当讲师，2021年8月至今在华南理工大学任副教授，2026年入选广东省自然科学基金杰出青年项目。研究兴趣包括计算流体力学、计算材料力学和人工智能优化算法。

报告人：李小舟副研究员（电子科技大学）

报告题目：Extracting more from numerical solutions: convolution-based reconstruction for accuracy enhancement

报告摘要：Numerical solutions may contain useful information that is not immediately visible from their pointwise accuracy or regularity. For certain discretizations, structured components of the numerical error retain higher-order information in weak, averaged, or locally combined forms. This raises a natural question: can such information be recovered from an already computed solution, without modifying or rerunning the original solver? This talk introduces convolution-based reconstruction techniques developed within the Smoothness-Increasing Accuracy-Conserving (SIAC) framework. Unlike conventional smoothing filters, these reconstructions use carefully designed kernels to preserve polynomial information while exploiting structures in the underlying discretization error. Under suitable conditions, the resulting representation can be both smoother and more accurate than the original numerical solution. We discuss the main principles behind the reconstruction, including what information it uses, which kernel properties are essential, and how it can be applied non-intrusively to data generated by existing numerical software.

报告时间：2026年11月15日11:00-12:00

报告地点：理学楼609室

报告人简介：李小舟，电子科技大学数学科学学院副研究员。本科毕业于中国科学技术大学数学系，获荷兰代尔夫特理工大学数学博士学位。主要从事微分方程数值方法与科学计算研究，近期关注如何利用数值近似中的误差结构，通过低成本、非侵入式重构改善应用相关输出。研究工作涉及高阶DG方法、超收敛后处理与高性能计算。