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.

引用

页码：180 / 194

页数：15

共 50 条

[21] Maximal regularity of discrete and continuous time evolution equations
Blunck, S
STUDIA MATHEMATICA, 2001, 146 (02) : 157 - 176
[22] Semilinear evolution equations on discrete time and maximal regularity
Cuevas, Claudio
Lizama, Carlos
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2010, 361 (01) : 234 - 245
[23] Discrete maximum principle for interior penalty discontinuous Galerkin methods
Horvath, Tamas L.
Mincsovics, Miklos E.
CENTRAL EUROPEAN JOURNAL OF MATHEMATICS, 2013, 11 (04): : 664 - 679
[24] TIME-DISCRETE NETWORKS
DVORAK, V
ELECTRONICS LETTERS, 1968, 4 (11) : 222 - &
[25] ON A POSTERIORI ERROR ESTIMATES FOR SPACE TIME DISCONTINUOUS GALERKIN METHOD
Dolejsi, Vit
Roskovec, Filip
Vlasak, Miloslav
PROCEEDINGS OF THE CONFERENCE ALGORITMY 2016, 2016, : 125 - 134
[26] Error analysis of discontinuous Galerkin methods for the Stokes problem under minimal regularity
Badia, S.
Codina, R.
Gudi, T.
Guzman, J.
IMA JOURNAL OF NUMERICAL ANALYSIS, 2014, 34 (02) : 800 - 819
[27] Optimal Order Error Estimates for Discontinuous Galerkin Methods for the Wave Equation
Han, Weimin
He, Limin
Wang, Fei
JOURNAL OF SCIENTIFIC COMPUTING, 2019, 78 (01) : 121 - 144
[28] A POSTERIORI ERROR ESTIMATES FOR DISCONTINUOUS GALERKIN METHODS ON POLYGONAL AND POLYHEDRAL MESHES
Cangiani, Andrea
Dong, Zhaonan
Georgoulis, Emmanuil H.
SIAM JOURNAL ON NUMERICAL ANALYSIS, 2023, 61 (05) : 2352 - 2380
[29] L∞ error estimates of discontinuous Galerkin methods for delay differential equations
Li, Dongfang
Zhang, Chengjian
APPLIED NUMERICAL MATHEMATICS, 2014, 82 : 1 - 10
[30] A posteriori error estimates for local discontinuous Galerkin methods of linear elasticity
Chen, Yun-Cheng
Huang, Jian-Guo
Xu, Yi-Feng
Shanghai Jiaotong Daxue Xuebao/Journal of Shanghai Jiaotong University, 2011, 45 (12): : 1857 - 1862

← 1 2 3 4 5 →