Robust a priori and a posteriori error analysis for the approximation of Allen–Cahn and Ginzburg–Landau equations past topological changes [PDF]
, 2010 A priori and a posteriori error estimates are derived for the numerical approximation of scalar and complex valued phase field models. Particular attention is devoted to the dependence of the estimates on a small parameter and to the validity of the ...
Rüdiger Müller +11 more
core +1 more source
A priori estimates for fluid interface problems [PDF]
Communications on Pure and Applied Mathematics, 2008 AbstractWe consider the regularity of an interface between two incompressible and inviscid fluid flows in the presence of surface tension. We obtain local‐in‐time estimates on the interface in H(3/2)k + 1 and the velocity fields in H(3/2)k. These estimates are obtained using geometric considerations which show that the Kelvin‐Helmholtz instabilities ...
Shatah, Jalal, Zeng, Chongchun
openaire +3 more sources
A priori error estimates for energy-based quasicontinuum approximations of a periodic chain [PDF]
, 2011 We derive a priori error estimates for three prototypical energy-based quasicontinuum (QC) methods: the local QC method, the energy-based QC method, and the quasi-nonlocal QC method.
Christoph Ortner +3 more
core +1 more source
, 2023 We consider a semilinear boundary value problem −Δu =f(x,u), in Ω, with Dirichlet boundary conditions, where Ω ⊂ RN with N > 2, is a bounded smooth domain, and f is a Carathéodory function, superlinear and subcritical at infinity.
Pardo San Gil, Rosa María
core +1 more source
A priori and a posteriori analysis of the quasinonlocal quasicontinuum method in 1D [PDF]
, 2010 For a next-nearest neighbour pair interaction model in a periodic domain, a priori and a posteriori analyses of the quasinonlocal quasicontinuum method (QNL-QC) are presented.
Christoph Ortner, Ortner, Christoph
core +1 more source
Analysis of an energy-based atomistic/continuum approximation of a vacancy in the 2D triangular lattice [PDF]
, 2013 We present an a priori error analysis of a practical energy based atomistic/continuum coupling method (A. V. Shapeev, Multiscale Model. Simul., 9(3):905-932, 2011) in two dimensions, for finite-range pair-potential interactions, in the presence of ...
Ortner, C. +2 more
core +1 more source
Weighted a priori estimates for the Poisson equation [PDF]
Indiana University Mathematics Journal, 2008 and let u be a solution of the classical Poisson problem in Ω; i.e., -Δu = f in Ω, u = 0 on ∂Ω, where f ∈ L ρ ω (Ω) and ω is a weight in Ap. The main goal of this paper is to prove the following a priori estimate ∥u∥W 2,p ω (Ω)≤C∥f∥L p ω (Ω), and to give some applications for weights given by powers of the distance to the boundary.
Durán, Ricardo Guillermo +2 more
openaire +3 more sources
A priori error analysis of two force-based atomistic/continuum models of a periodic chain [PDF]
, 2011 The force-based quasicontinuum (QCF) approximation is a non-conservative atomistic/continuum hybrid model for the simulation of defects in crystals. We present an a priori error analysis of the QCF method, applied to a one-dimensional periodic chain ...
Makridakis , C. +9 more
core +1 more source
A priori estimates of solutions of superlinear problems [PDF]
, 2001 summary:In this survey we consider superlinear parabolic problems which possess both blowing-up and global solutions and we study a priori estimates of global ...
Quittner, Pavol
core +1 more source
On the fully discrete approximations of the MGT two-temperatures thermoelastic problem
Archives of Mechanics, 2022 We consider a one-dimensional two-temperatures thermoelastic model. The corresponding variational problem leads to a coupled system which is written in terms of the mechanical velocity, the temperature speed and the inductive temperature.
J. Baldonedo +2 more
doaj +1 more source