论文标题
广义Korn的分段不平等$ H^2 $向量字段
Generalized Korn's Inequalities for Piecewise $H^2$ Vector Fields
论文作者
论文摘要
本文的目的是在三维空间中构建一类新的分段H2矢量场的Korn不平等现象。由此产生的Korn的不平等与标准Korn的不等式不同，因为它们涉及无微量的对称梯度操作员，代替了通常的对称梯度操作员。预计新的广义Korn的不平等现象将有助于分析广泛的有限元方法，包括混合有限元方法和不连续的Galerkin方法。
The purpose of this paper is to construct a new class of discrete generalized Korn's inequalities for piecewise H2 vector fields in three-dimensional space. The resulting Korn's inequalities are different from the standard Korn's inequalities, as they involve the trace-free symmetric gradient operator, in place of the usual symmetric gradient operator. It is anticipated that the new generalized Korn's inequalities will be useful for the analysis of a broad range of finite element methods, including mixed finite element methods and discontinuous Galerkin methods.
