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A Moving Mesh Method Based on the Geometric Conservation Law
TLDR
A new adaptive mesh movement strategy is presented, which, unlike many existing moving mesh methods, targets the mesh velocities rather than the mesh coordinates, and bears a close relation with the Lagrangian method.
A two-dimensional spectrum analysis for sedimentation velocity experiments of mixtures with heterogeneity in molecular weight and shape
TLDR
This work reports a model-independent analysis approach for fitting sedimentation velocity data which permits simultaneous determination of shape and molecular weight distributions for mono- and polydisperse solutions of macromolecules and shows that it can be used to identify modes of aggregation and slow polymerization.
An Interpolation Error Estimate on Anisotropic Meshes in Rn and Optimal Metrics for Mesh Refinement
  • Weiming Cao
  • Computer Science, Mathematics
    SIAM J. Numer. Anal.
  • 1 October 2007
TLDR
Numerical results show that the smallest interpolation error is attained exactly on meshes optimal for the corresponding error norm as predicted.
Anr-Adaptive Finite Element Method Based upon Moving Mesh PDEs
TLDR
A fully developedr-adaptive finite element method can be expected to be ideally suited to complement the currently popularh-pfinite element methods and to provide increased reliability and efficiency for mesh adaptation.
Modeling analytical ultracentrifugation experiments with an adaptive space-time finite element solution of the Lamm equation.
TLDR
Compared to the widely used finite element method by Claverie and the moving hat method by Schuck, the ASTFEM method is not only more accurate but also free from the oscillation around the cell bottom for any somega(2)/D without any increase in computational effort.
A Study of Monitor Functions for Two-Dimensional Adaptive Mesh Generation
TLDR
A general strategy is suggested for how to choose the monitor function, and numerical results are presented for illustrative purposes.
Approaches for generating moving adaptive meshes: location versus velocity
A variety of approaches for generating moving adaptive methods are summarized and compared. They basically fall into two groups: the velocity and the location based methods. The features, including
On the Error of Linear Interpolation and the Orientation, Aspect Ratio, and Internal Angles of a Triangle
  • Weiming Cao
  • Computer Science, Mathematics
    SIAM J. Numer. Anal.
  • 2005
TLDR
Two exact formulas are derived for the H^1-seminorm and L^2-norm of the interpolation error in terms of the area, aspect ratio, orientation, and internal angles of the triangle to reveal the precise relation between the error of linear interpolation on a general triangle and the geometric characters of the Triangle.
An interpolation error estimate in &Ropf2 based on the anisotropic measures of higher order derivatives
  • Weiming Cao
  • Mathematics, Computer Science
    Math. Comput.
  • 2008
TLDR
An anisotropic error estimate is derived for the piecewise polynomial interpolation over a family of triangulations that are quasi-uniform under a given Riemannian metric.
A two-dimensional moving finite element method with local refinement based on a posteriori error estimates
In this paper, we consider the numerical solution of time-dependent PDEs using a finite element method based upon rh-adaptivity. An adaptive horizontal method of lines strategy equipped with a
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