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6 papers · 2 filters
Iterative Methods for the Force-based Quasicontinuum Approximation
Matthew Dobson, Mitchell Luskin, Christoph Ortner
Force-based atomistic-continuum hybrid methods are the only known pointwise consistent methods for coupling a general atomistic model to a finite element continuum model. For this…
Numerical analysis of the planewave discretization of orbital-free and Kohn-Sham models Part I: The Thomas-Fermi-von Weizacker model
Eric Cancès, Rachida Chakir, Yvon Maday
We provide {\it a priori} error estimates for the spectral and pseudospectral Fourier (also called planewave) discretizations of the periodic Thomas-Fermi-von Weizsäcker (TFW) mode…
Existence and approximation of a (regularized) Oldroyd-B model
John W. Barrett, Sebastien Boyaval
Two finite element approximations of the Oldroyd-B model for dilute polymeric fluids are considered, in bounded 2- and 3-dimensional domains, under no flow boundary conditions. The…
An energy-preserving Discrete Element Method for elastodynamics
Laurent Monasse, Christian Mariotti
We develop a Discrete Element Method (DEM) for elastodynamics using polyhedral elements. We show that for a given choice of forces and torques, we recover the equations of linear e…
Numerical analysis of nonlinear eigenvalue problems
Eric Cancès, Rachida Chakir, Yvon Maday
We provide a priori error estimates for variational approximations of the ground state eigenvalue and eigenvector of nonlinear elliptic eigenvalue problems of the form $-{div} (A\n…
Stability, Instability, and Error of the Force-based Quasicontinuum Approximation
Matthew Dobson, Mitchell Luskin, Christoph Ortner
Due to their algorithmic simplicity and high accuracy, force-based model coupling techniques are an exciting development in computational physics. For example, the force-based quas…