TY - JOUR
T1 - A Full Space-Time Convergence Order Analysis of Operator Splittings for Linear Dissipative Evolution Equations
JO - Communications in Computational Physics
VL - 5
SP - 1302
EP - 1316
PY - 2018
DA - 2018/04
SN - 19
DO - http://doi.org/10.4208/cicp.scpde14.22s
UR - https://global-sci.org/intro/article_detail/cicp/11130.html
KW - 
AB - <p style="text-align: justify;">The Douglas-Rachford and Peaceman-Rachford splitting methods are common
choices for temporal discretizations of evolution equations. In this paper we combine
these methods with spatial discretizations fulfilling some easily verifiable criteria.
In the setting of linear dissipative evolution equations we prove optimal convergence
orders, simultaneously in time and space. We apply our abstract results to dimension
splitting of a 2D diffusion problem, where a finite element method is used for spatial
discretization. To conclude, the convergence results are illustrated with numerical
experiments.</p>