主持人：郑海标
报告摘要：
In this work, we primarily focus on the Q1 finite element spaces in any finite dimension, equipped with the discrete \ell_h^2 inner product induced by the simple row-sum mass lumping. We establish the uniform (with respect to the mesh size h) equivalence between the discrete \ell_h^2 norm and the L^2 norm on these spaces, for both uniform and nonuniform meshes. Our main contribution is the derivation of sharp bounds for the equivalence between these two norms. Numerical examples demonstrate that these bounds are indeed sharp. Furthermore, we establish the equivalence between the discrete h_h^1 norm and the continuous H^1 norm, along with corresponding numerical results. As an application, we also provide the equivalence between discrete and continuous norms in the context of error estimates for central FD solutions on polygonal domains.
报告人简介：
冯新龙，二级教授，博士生导师。研究领域为计算数学、计算流体力学、不确定性量化、人工智能与机器学习等。主持完成多项国家自然科学基金项目，在SIAM、IEEE等国际著名期刊合作发表学术论文百余篇。新疆大学副校长，国家级人才计划入选者。
