L∞(L2) and L∞(L∞) error estimates for mixed methods for integro-differential equations of parabolic type

Jiang, Ziwen. "L∞(L2) and L∞(L∞) error estimates for mixed methods for integro-differential equations of parabolic type." ESAIM: Mathematical Modelling and Numerical Analysis 33.3 (2010): 531-546. <http://eudml.org/doc/197498>.

@article{Jiang2010,
abstract = { Error estimates in L∞(0,T;L2(Ω)), L∞(0,T;L2(Ω)2), L∞(0,T;L∞(Ω)), L∞(0,T;L∞(Ω)2), Ω in $\{\mathbb R\}^2$, are derived for a mixed finite element method for the initial-boundary value problem for integro-differential equation $$u\_t=\{\rm div\}\\{a\bigtriangledown u+\int^t\_0b\_1\bigtriangledown u\{\rm d\}\tau +\int^t\_0\{\bf c\}u\{\rm d\}\tau\\}+f$$ based on the Raviart-Thomas space Vh x Wh ⊂ H(div;Ω) x L2(Ω). Optimal order estimates are obtained for the approximation of u,ut in L∞(0,T;L2(Ω)) and the associated velocity p in L∞(0,T;L2(Ω)2), divp in L∞(0,T;L2(Ω)). Quasi-optimal order estimates are obtained for the approximation of u in L∞(0,T;L∞(Ω)) and p in L∞(0,T;L∞(Ω)2. },
author = {Jiang, Ziwen},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = { Error estimates; mixed finite element; integro-differential equations; parabolic type.; mixed finite element method; initial-boundary value problems; parabolic integro-differential equation; error estimates},
language = {eng},
month = {3},
number = {3},
pages = {531-546},
publisher = {EDP Sciences},
title = {L∞(L2) and L∞(L∞) error estimates for mixed methods for integro-differential equations of parabolic type},
url = {http://eudml.org/doc/197498},
volume = {33},
year = {2010},
}

TY - JOUR
AU - Jiang, Ziwen
TI - L∞(L2) and L∞(L∞) error estimates for mixed methods for integro-differential equations of parabolic type
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2010/3//
PB - EDP Sciences
VL - 33
IS - 3
SP - 531
EP - 546
AB - Error estimates in L∞(0,T;L2(Ω)), L∞(0,T;L2(Ω)2), L∞(0,T;L∞(Ω)), L∞(0,T;L∞(Ω)2), Ω in ${\mathbb R}^2$, are derived for a mixed finite element method for the initial-boundary value problem for integro-differential equation $$u_t={\rm div}\{a\bigtriangledown u+\int^t_0b_1\bigtriangledown u{\rm d}\tau +\int^t_0{\bf c}u{\rm d}\tau\}+f$$ based on the Raviart-Thomas space Vh x Wh ⊂ H(div;Ω) x L2(Ω). Optimal order estimates are obtained for the approximation of u,ut in L∞(0,T;L2(Ω)) and the associated velocity p in L∞(0,T;L2(Ω)2), divp in L∞(0,T;L2(Ω)). Quasi-optimal order estimates are obtained for the approximation of u in L∞(0,T;L∞(Ω)) and p in L∞(0,T;L∞(Ω)2.
LA - eng
KW - Error estimates; mixed finite element; integro-differential equations; parabolic type.; mixed finite element method; initial-boundary value problems; parabolic integro-differential equation; error estimates
UR - http://eudml.org/doc/197498
ER -