A Posteriori L∞(L2)

被引：2
作者：
Sabawi, Younis A. [1 ,2 ]
机构：
[1] Koya Univ, Fac Sci & Hlth, Dept Math, Koya KOY45, Erbil Fr, Iraq
[2] Tishk Int Univ, Fac Educ, Dept Math Educ, Erbil, Iraq
来源：
BAGHDAD SCIENCE JOURNAL | 2021年 / 18卷 / 03期
关键词：
A posteriori error estimates; Discontinuous Galerkin methods; Interface semilinear parabolic problems; DISCONTINUOUS GALERKIN METHODS; ERROR ESTIMATION; PARABOLIC EQUATIONS; MASS-TRANSFER; MAXIMUM NORM; BLOW-UP;
D O I：
10.21123/bsj.2021.18.3.0522
中图分类号：
O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];
学科分类号：
07 ; 0710 ; 09 ;
摘要：
The aim of this paper is to derive a posteriori error estimates for semilinear parabolic interface problems. More specifically, optimal order a posteriori error analysis in the L-infinity(L-2) + L-2(H-1)- norm for semidiscrete semilinear parabolic interface problems is derived by using elliptic reconstruction technique introduced by Makridakis and Nochetto in (2003). A key idea for this technique is the use of error estimators derived for elliptic interface problems to obtain parabolic estimators that are of optimal order in space and time.
引用
收藏
页码：522 / 530
页数：9
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共 30 条
  • [1] A posteriori error estimation for the finite element method-of-lines solution of parabolic problems
    Adjerid, S
    Flaherty, JE
    Babuska, I
    [J]. MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES, 1999, 9 (02) : 261 - 286
  • [2] Optimal order a posteriori error estimates for a class of Runge-Kutta and Galerkin methods
    Akrivis, Georgios
    Makridakis, Charalambos
    Nochetto, Ricardo H.
    [J]. NUMERISCHE MATHEMATIK, 2009, 114 (01) : 133 - 160
  • [3] A POSTERIORI ERROR CONTROL FOR FULLY DISCRETE CRANK-NICOLSON SCHEMES
    Baensch, E.
    Karakatsani, F.
    Makridakis, Ch.
    [J]. SIAM JOURNAL ON NUMERICAL ANALYSIS, 2012, 50 (06) : 2845 - 2872
  • [4] hp-adaptive discontinuous Galerkin methods for non-stationary convection-diffusion problems
    Cangiani, A.
    Georgoulis, E. H.
    Giani, S.
    Metcalfe, S.
    [J]. COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2019, 78 (09) : 3090 - 3104
  • [5] Revealing new dynamical patterns in a reaction-diffusion model with cyclic competition via a novel computational framework
    Cangiani, A.
    Georgoulis, E. H.
    Morozov, A. Yu.
    Sutton, O. J.
    [J]. PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, 2018, 474 (2213):
  • [6] Convergence of an adaptive discontinuous Galerkin method for elliptic interface problems
    Cangiani, Andrea
    Georgoulis, Emmanuil H.
    Sabawi, Younis A.
    [J]. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2020, 367
  • [7] ADAPTIVE DISCONTINUOUS GALERKIN METHODS FOR ELLIPTIC INTERFACE PROBLEMS
    Cangiani, Andrea
    Georgoulis, Emmanuil H.
    Sabawi, Younis A.
    [J]. MATHEMATICS OF COMPUTATION, 2018, 87 (314) : 2675 - 2707
  • [8] ADAPTIVITY AND BLOW-UP DETECTION FOR NONLINEAR EVOLUTION PROBLEMS
    Cangiani, Andrea
    Georgoulis, Emmanuil H.
    Kyza, Irene
    Metcalfe, Stephen
    [J]. SIAM JOURNAL ON SCIENTIFIC COMPUTING, 2016, 38 (06) : A3833 - A3856
  • [9] Discontinuous Galerkin methods for fast reactive mass transfer through semi-permeable membranes
    Cangiani, Andrea
    Georgoulis, Emmanuil H.
    Jensen, Max
    [J]. APPLIED NUMERICAL MATHEMATICS, 2016, 104 : 3 - 14
  • [10] DISCONTINUOUS GALERKIN METHODS FOR MASS TRANSFER THROUGH SEMIPERMEABLE MEMBRANES
    Cangiani, Andrea
    Georgoulis, Emmanuil H.
    Jensen, Max
    [J]. SIAM JOURNAL ON NUMERICAL ANALYSIS, 2013, 51 (05) : 2911 - 2934
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