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

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

- Volume: 33, Issue: 3, page 531-546
- ISSN: 0764-583X

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topJiang, 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 -

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