ON MAXIMAL REGULARITY ESTIMATES FOR DISCONTINUOUS GALERKIN TIME-DISCRETE METHODS

被引：3
|
作者：
Akrivis, Georgios [1 ,2 ]
Makridakis, Charalambos [2 ,3 ,4 ]
机构：
[1] Univ Ioannina, Dept Comp Sci & Engn, Ioannina 45110, Greece
[2] Fdn Res & Technol Hellas FORTH, Inst Appl & Computat Math, Iraklion 70013, Crete, Greece
[3] Univ Crete, Dept Math & Appl Math, Modeling & Sci Comp, Iraklion 70013, Crete, Greece
[4] Univ Sussex, MPS, Brighton BN1 9QH, E Sussex, England
来源：
SIAM JOURNAL ON NUMERICAL ANALYSIS | 2022年 / 60卷 / 01期
关键词：
a posteriori error estimates; discontinuous Galerkin methods; parabolic equations; maximal parabolic regularity; discrete maximal parabolic regularity; Radau IIA methods; FOURIER MULTIPLIER THEOREMS; FINITE-ELEMENT METHODS; PARABOLIC EQUATIONS; DISCRETIZATIONS;
D O I：
10.1137/20M1383781
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We consider the discretization of differential equations satisfying the maximal parabolic L-P-regularity property in Banach spaces by discontinuous Galerkin methods. We use the maximal regularity framework to establish that the discontinuous Galerkin methods preserve the maximal L-P-regularity, satisfy corresponding a posteriori error estimates, and the estimators are of optimal asymptotic order of convergence. In our proofs, we use a suitable interpretation of the discontinuous Galerkin methods as modified Radau IIA methods.
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页码：180 / 194
页数：15
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