Minimal residual space-time discretizations of parabolic equations: Asymmetric spatial operators. (1st November 2021)

• Record Type: Journal Article
• Authors: Stevenson, Rob; Westerdiep, Jan
• Is Part Of: Computers & mathematics with applications. Volume 101(2021)
• Page Start: 107
• Page End: 118
• Publication Date: 2021-11-01
• Subjects: Parabolic PDEs -- Space-time variational formulations -- Quasi-best approximations -- Stability -- Robustness; Electronic data processing -- Periodicals; Mathematics -- Data processing -- Periodicals; 510.28541
• DOI: 10.1016/j.camwa.2021.09.014
• Languages: English
• ISSNs: 0898-1221

Abstract

Abstract: 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.