Continuous Mesh Framework Part II: Validations and Applications

This paper gives a numerical validation of the continuous mesh framework introduced in Part I [23]. We numerically show that the interpolation error can be evaluated analytically once analytical expressions of a mesh and a function are given. In particular, the strong duality between discrete and continuous views for the interpolation error is emphasized on 2D and 3D examples. In addition, we show the ability of this framework to predict the order of convergence, given a specific adaptive strategy defined by a sequence of continuous meshes. The continuous mesh concept is then used to devise an adaptive strategy to control the Lp norm of the continuous interpolation error. Given the Lp norm of the continuous interpolation error, we derive the optimal continuous mesh minimizing this error. This exemplifies the potential of this framework as we use a calculus of variations that is not defined on the space of discrete meshes. Anisotropic adaptations on analytical functions correlate th...

• Type: Journal
• Year: 2011
• Where: SIAMNUM
• Authors: Adrien Loseille, Frédéric Alauzet
• Keywords: Continuous Interpolation Error, Continuous Mesh, Interpolation Error, SIAMNUM 2011