TY - JOUR
T1 - Implementation of Some Methods of Shape Design for Variational Inequalities
AU - Butt , Rizwan
JO - Journal of Partial Differential Equations
VL - 2
SP - 122
EP - 137
PY - 2013
DA - 2013/06
SN - 26
DO - http://doi.org/10.4208/jpde.v26.n2.3
UR - https://global-sci.org/intro/article_detail/jpde/5157.html
KW - Sobolev space
KW - convexity
KW - optimal shape design
KW - variational inequalities
KW - approximation
KW - optimization techniques
KW - finite element method
KW - material derivative method
AB - <p>In this paper we present some results concerning the optimal shape design problem governed by the fourth-order variational inequalities. The problem can be considered as a model example for the design of the shapes for elastic-plastic problem. The computations are done by finite element method, and the performance criterion is minimized by the material derivative method. We also discuss the error estimates in the appropriate norm and present some numerical results. An example is used to clearly illustrate the essential elements of shape design problems.</p>