TY - JOUR
T1 - Convergence of Rothe Scheme for Hemivariational Inequalities of Parabolic Type
AU - P. Kalita
JO - International Journal of Numerical Analysis and Modeling
VL - 2
SP - 445
EP - 465
PY - 2013
DA - 2013/10
SN - 10
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/ijnam/577.html
KW - hemivariational inequality, Rothe method, convergence, existence.
AB - <p style="text-align: justify;">This article presents the convergence analysis of a sequence of piecewise constant and
piecewise linear functions obtained by the Rothe method to the solution of the first order evolution
partial differential inclusion $u&#39;(t)+Au(t)+\iota^{*}&nbsp;∂ J(\iota u(t)) \ni f(t)$, where the multivalued term is given
by the Clarke subdifferential of a locally Lipschitz functional. The method provides the proof of
existence of solutions alternative to the ones known in literature and together with any method for
underlying elliptic problem, can serve as the effective tool to approximate the solution numerically.
Presented approach puts into the unified framework known results for multivalued nonmonotone
source term and boundary conditions, and generalizes them to the case where the multivalued
term is defined on the arbitrary reflexive Banach space as long as appropriate conditions are
satisfied. In addition, the results on improved convergence as well as the numerical examples are
presented.</p>