报告人：冯新龙 教授（新疆大学）

时间：2026年4月17日 15:30-

地点：数统学院LD703

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.

邀请人：王坤

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