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Error Estimates for the Adaptive Computation of a Scalar Three Well Problem
Author(s) -
Bartels S.
Publication year - 2002
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/1617-7061(200203)1:1<502::aid-pamm502>3.0.co;2-r
Subject(s) - a priori and a posteriori , scalar (mathematics) , computation , mathematics , regular polygon , mathematical optimization , measure (data warehouse) , scalar field , set (abstract data type) , algorithm , computer science , geometry , mathematical physics , philosophy , epistemology , database , programming language
We investigate the numerical approximation of Young measure solutions appearing as generalised solutions in scalar non‐convex variational problems. A priori and a posteriori error estimates for a macroscopic quantity, i.e., the stress, are given. Numerical experiments for a scalar three well problem, occurring as a subproblem in the theory of phase transitions in crystalline solids, show that the computational effort can be significantly reduced using an adaptive mesh‐refinement strategy combined with an active set technique by Carstensen and Roubíček.