An adaptive finite element method for solving a double well problem describing crystalline microstructure

Prohl, Andreas. "An adaptive finite element method for solving a double well problem describing crystalline microstructure." ESAIM: Mathematical Modelling and Numerical Analysis 33.4 (2010): 781-796. <http://eudml.org/doc/197413>.

@article{Prohl2010,
abstract = { The minimization of nonconvex functionals naturally arises in materials sciences where deformation gradients in certain alloys exhibit microstructures. For example, minimizing sequences of the nonconvex Ericksen-James energy can be associated with deformations in martensitic materials that are observed in experiments[2,3]. — From the numerical point of view, classical conforming and nonconforming finite element discretizations have been observed to give minimizers with their quality being highly dependent on the underlying triangulation, see [8,24,26,27] for a survey. Recently, a new approach has been proposed and analyzed in [15,16] that is based on discontinuous finite elements to reduce the pollution effect of a general triangulation on the computed minimizer. The goal of the present paper is to propose and analyze an adaptive method, giving a more accurate resolution of laminated microstructure on arbitrary grids. },
author = {Prohl, Andreas},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Adaptive algorithm; finite element method; nonconvex minimization; multi-well problem; microstructure; multiscale; nonlinear elasticity; shape-memory alloy; materials science.; nonconvex energy functional; laminated microstructure; improved convergence; discontinuous ansatz functions; adaptivity criterion; height of interelement jumps},
language = {eng},
month = {3},
number = {4},
pages = {781-796},
publisher = {EDP Sciences},
title = {An adaptive finite element method for solving a double well problem describing crystalline microstructure},
url = {http://eudml.org/doc/197413},
volume = {33},
year = {2010},
}

TY - JOUR
AU - Prohl, Andreas
TI - An adaptive finite element method for solving a double well problem describing crystalline microstructure
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2010/3//
PB - EDP Sciences
VL - 33
IS - 4
SP - 781
EP - 796
AB - The minimization of nonconvex functionals naturally arises in materials sciences where deformation gradients in certain alloys exhibit microstructures. For example, minimizing sequences of the nonconvex Ericksen-James energy can be associated with deformations in martensitic materials that are observed in experiments[2,3]. — From the numerical point of view, classical conforming and nonconforming finite element discretizations have been observed to give minimizers with their quality being highly dependent on the underlying triangulation, see [8,24,26,27] for a survey. Recently, a new approach has been proposed and analyzed in [15,16] that is based on discontinuous finite elements to reduce the pollution effect of a general triangulation on the computed minimizer. The goal of the present paper is to propose and analyze an adaptive method, giving a more accurate resolution of laminated microstructure on arbitrary grids.
LA - eng
KW - Adaptive algorithm; finite element method; nonconvex minimization; multi-well problem; microstructure; multiscale; nonlinear elasticity; shape-memory alloy; materials science.; nonconvex energy functional; laminated microstructure; improved convergence; discontinuous ansatz functions; adaptivity criterion; height of interelement jumps
UR - http://eudml.org/doc/197413
ER -