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Morley–Wang–Xu Element
In applied mathematics, the Morlely–Wang–Xu (MWX) element is a canonical construction of a family of piecewise polynomials with the minimal degree elements for any 2m-th order of elliptic and parabolic equations in any spatial-dimension \mathbb^n for 1\leq m \leq n. The MWX element provides a consistent approximation of Sobolev space H^m in \mathbb^n. Morley–Wang–Xu element The Morley–Wang–Xu element (T,P_T,D_T) is described as follows. T is a simplex and P_T = P_m(T) . The set of degrees of freedom will be given next. Given an n-simplex T with vertices a_i, for 1\leq k\leq n, let \mathcal_ be the set consisting of all (n-k)-dimensional subsimplexe of T. For any F \in \mathcal_, let , F, denote its measure, and let \nu_, \cdots, \nu_ be its unit outer normals which are linearly independent. For 1\leq k\leq m, any (n-k)-dimensional subsimplex F\in \mathcal_ and \beta\in A_k with , \beta, =m-k, define : d_(v) = \frac\int_F \frac. The degrees of freedom are depicte ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sobolev Space
In mathematics, a Sobolev space is a vector space of functions equipped with a norm that is a combination of ''Lp''-norms of the function together with its derivatives up to a given order. The derivatives are understood in a suitable weak sense to make the space complete, i.e. a Banach space. Intuitively, a Sobolev space is a space of functions possessing sufficiently many derivatives for some application domain, such as partial differential equations, and equipped with a norm that measures both the size and regularity of a function. Sobolev spaces are named after the Russian mathematician Sergei Sobolev. Their importance comes from the fact that weak solutions of some important partial differential equations exist in appropriate Sobolev spaces, even when there are no strong solutions in spaces of continuous functions with the derivatives understood in the classical sense. Motivation In this section and throughout the article \Omega is an open subset of \R^n. There are many c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
MWX Table
MWX may refer to: * Morley–Wang–Xu element In applied mathematics, the Morlely–Wang–Xu (MWX) element is a canonical construction of a family of piecewise polynomials with the minimal degree elements for any 2m-th order of elliptic and parabolic equations in any spatial-dimension \mathb ..., a canonical construction in applied mathematics * Muan International Airport (IATA: MWX), South Jeolla Province, South Korea {{Disambiguation ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jinchao Xu
Jinchao Xu (许进超, born 1961) is an American-Chinese mathematician. He is currently the Verne M. Willaman Professor in the Department of Mathematics at the Pennsylvania State University, University Park. He is known for his work on multigrid methods, domain decomposition methods, finite element methods, and more recently deep neural networks. Academic Biography Xu received his bachelor's degree from the Xiangtan University in 1982, his master's degree from the Peking University in 1984, and his doctoral degree from the Cornell University in 1989. He joined the Pennsylvania State University (Penn State) in 1989 as assistant professor of mathematics, was promoted to associate professor in 1991, and to professor in 1995. He was named a Distinguished Professor of Mathematics in 2007, the Francis R. and Helen M. Pentz Professor of Science in 2010, and the Verne M. Willaman Professor of Mathematics in 2015. He is currently the director of the Center for Computational Mathematic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
MWX Fig
MWX may refer to: * Morley–Wang–Xu element In applied mathematics, the Morlely–Wang–Xu (MWX) element is a canonical construction of a family of piecewise polynomials with the minimal degree elements for any 2m-th order of elliptic and parabolic equations in any spatial-dimension \mathb ..., a canonical construction in applied mathematics * Muan International Airport (IATA: MWX), South Jeolla Province, South Korea {{Disambiguation ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
