TY - JOUR
T1 - Space-time approximation of stochastic p-Laplace type systems
AU - Breit, Dominic
AU - Hofmanová, Martina
AU - Loisel, Sebastien
N1 - Funding Information:
\ast Received by the editors April 27, 2020; accepted for publication (in revised form) May 6, 2021; published electronically August 12, 2021. https://doi.org/10.1137/20M1334310 Funding: The work of the second author was supported by the German Science Foundation DFG via the Collaborative Research Center grant SFB1283. \dagger Department of Mathematics, Heriot-Watt University, Edinburgh, EH14 4AS, UK (d.breit@hw. ac.uk, [email protected]). \ddagger University Bielefeld, D-33501, Bielefeld, Germany ([email protected]).
Publisher Copyright:
© 2021 Society for Industrial and Applied Mathematics.
PY - 2021/8/12
Y1 - 2021/8/12
N2 - We consider systems of stochastic evolutionary equations of p-Laplace type. We establish convergence rates for a finite-element-based space-time approximation, where the error is measured in a suitable quasi-norm. Under natural regularity assumptions on the solution, our main result provides linear convergence in space and convergence of order (almost) 1/2 in time. The key ingredient of our analysis is a random time-grid, which allows us to compensate for the lack of time regularity. Our theoretical results are confirmed by numerical experiments.
AB - We consider systems of stochastic evolutionary equations of p-Laplace type. We establish convergence rates for a finite-element-based space-time approximation, where the error is measured in a suitable quasi-norm. Under natural regularity assumptions on the solution, our main result provides linear convergence in space and convergence of order (almost) 1/2 in time. The key ingredient of our analysis is a random time-grid, which allows us to compensate for the lack of time regularity. Our theoretical results are confirmed by numerical experiments.
KW - Finite element methods
KW - Nonlinear Laplace-type systems
KW - Parabolic stochastic PDEs
KW - Space-time discretization
UR - http://www.scopus.com/inward/record.url?scp=85113282993&partnerID=8YFLogxK
U2 - 10.1137/20M1334310
DO - 10.1137/20M1334310
M3 - Article
SN - 0036-1429
VL - 59
SP - 2218
EP - 2236
JO - SIAM Journal on Numerical Analysis
JF - SIAM Journal on Numerical Analysis
IS - 4
ER -