## Construction and application of algebraic dual polynomial representations for finite element methods. (arXiv:1712.09472v1 [math.NA])

Given a polynomial basis $\Psi_i$ which spans the polynomial vector space $\mathcal{P}$, this paper addresses the construction and use of the algebraic dual space $\mathcal{P}'$ and its canonical basis. Differentiation of dual variables will be discussed. The method will be applied to a Dirichlet and Neumann problem presented in \cite{CarstensenDemkowiczGopalakrishnan} and it is shown that the finite dimensional approximations satisfy $\phi^h = \mbox{div}\, \mathbf{q}^h$ on any grid. The dual method is also applied to a constrained minimization problem, which leads to a mixed finite element formulation. The discretization of the constraint and the Lagrange multiplier will be independent of the grid size, grid shape and the polynomial degree of the basis functions.查看全文

## Solidot 文章翻译

 你的名字 留空匿名提交 你的Email或网站 用户可以联系你 标题 简单描述 内容 Given a polynomial basis $\Psi_i$ which spans the polynomial vector space $\mathcal{P}$, this paper addresses the construction and use of the algebraic dual space $\mathcal{P}'$ and its canonical basis. Differentiation of dual variables will be discussed. The method will be applied to a Dirichlet and Neumann problem presented in \cite{CarstensenDemkowiczGopalakrishnan} and it is shown that the finite dimensional approximations satisfy $\phi^h = \mbox{div}\, \mathbf{q}^h$ on any grid. The dual method is also applied to a constrained minimization problem, which leads to a mixed finite element formulation. The discretization of the constraint and the Lagrange multiplier will be independent of the grid size, grid shape and the polynomial degree of the basis functions.