Minimal residual space-time discretizations of parabolic equations: Asymmetric spatial operators

被引：9
|
作者：
Stevenson, Rob [1 ]
Westerdiep, Jan [1 ]
机构：
[1] Univ Amsterdam, Korteweg de Vries KdV Inst Math, POB 94248, NL-1090 GE Amsterdam, Netherlands
来源：
COMPUTERS & MATHEMATICS WITH APPLICATIONS | 2021年 / 101卷
关键词：
Parabolic PDEs; Space-time variational formulations; Quasi-best approximations; Stability; Robustness; FINITE-ELEMENT-METHOD; BOUNDARY-CONDITIONS; STABILIZATION;
D O I：
10.1016/j.camwa.2021.09.014
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We consider a minimal residual discretization of a simultaneous space-time variational formulation of parabolic evolution equations. Under the usual 'LBB' stability condition on pairs of trial-and test spaces we show quasi optimality of the numerical approximations without assuming symmetry of the spatial part of the differential operator. Under a stronger LBB condition we show error estimates in an energy-norm that are independent of this spatial differential operator.
引用
收藏
页码：107 / 118
页数：12
相关论文
共 50 条
  • [41] UNSTRUCTURED SPACE-TIME FINITE ELEMENT METHODS FOR OPTIMAL CONTROL OF PARABOLIC EQUATIONS
    Langer, Ulrich
    Steinbach, Olaf
    Troltzsch, Fredi
    Yang, Huidong
    SIAM JOURNAL ON SCIENTIFIC COMPUTING, 2021, 43 (02): : A744 - A771
  • [42] A SPACE-TIME MULTISCALE MORTAR MIXED FINITE ELEMENT METHOD FOR PARABOLIC EQUATIONS
    Jayadharan, Manu
    Kern, Michel
    Vohrali, Martin
    Yotov, Ivan
    SIAM JOURNAL ON NUMERICAL ANALYSIS, 2023, 61 (02) : 675 - 706
  • [43] Generalized multiscale finite element methods for space-time heterogeneous parabolic equations
    Chung, Eric T.
    Efendiev, Yalchin
    Leung, Wing Tat
    Ye, Shuai
    COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2018, 76 (02) : 419 - 437
  • [44] SPACE-TIME L∞-ESTIMATES FOR SOLUTIONS OF INFINITE HORIZON SEMILINEAR PARABOLIC EQUATIONS
    Casas, Eduardo
    Kunisch, Karl
    COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, 2025, 24 (04) : 482 - 506
  • [45] Space-time spectral method for two-dimensional semilinear parabolic equations
    Liu, Wenjie
    Sun, Jiebao
    Wu, Boying
    MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2016, 39 (07) : 1646 - 1661
  • [46] A POSTERIORI ANALYSIS FOR SPACE-TIME, DISCONTINUOUS IN TIME GALERKIN APPROXIMATIONS FOR PARABOLIC EQUATIONS IN A VARIABLE DOMAIN
    Antonopoulou, Dimitra
    Plexousakis, Michael
    ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE, 2019, 53 (02): : 523 - 549
  • [47] h-multigrid for space-time discontinuous Galerkin discretizations of the compressible Navier-Stokes equations
    Klaij, C. M.
    van Raalte, M. H.
    van der Ven, H.
    van der Vegt, J. J. W.
    JOURNAL OF COMPUTATIONAL PHYSICS, 2007, 227 (02) : 1024 - 1045
  • [48] The Cauchy Problem for Space-Time Monopole Equations in Temporal and Spatial Gauge
    Huh, Hyungjin
    Yim, Jihyun
    ADVANCES IN MATHEMATICAL PHYSICS, 2017, 2017
  • [49] CONJUGATIONS AND HERMITIAN OPERATORS IN SPACE-TIME
    SOBCZYK, G
    ACTA PHYSICA POLONICA B, 1981, 12 (06): : 509 - 521
  • [50] ON THE QUANTIZATION OF PHYSICAL SPACE-TIME OPERATORS
    WATANABE, I
    PROGRESS OF THEORETICAL PHYSICS, 1960, 24 (03): : 465 - 483
12345