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A posteriori error estimates for nonlinear problems: L r , (0, T ; W 1,ρ (Ω))‐error estimates for finite element discretizations of parabolic equations
Author(s) -
Verfürth R.
Publication year - 1998
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/(sici)1098-2426(199807)14:4<487::aid-num4>3.0.co;2-g
Subject(s) - mathematics , backward euler method , finite element method , estimator , partial differential equation , a priori and a posteriori , crank–nicolson method , nonlinear system , scalar (mathematics) , parabolic partial differential equation , mathematical analysis , euler equations , numerical analysis , geometry , philosophy , physics , epistemology , quantum mechanics , thermodynamics , statistics
Using the abstract framework of [R. Verfürth, Math. Comput. 62, 445–475 (1996)], we analyze a residual a posteriori error estimator for space‐time finite element discretizations of parabolic PDEs. The estimator gives global upper and local lower bounds on the error of the numerical solution. The finite element discretizations in particular cover the so‐called θ‐scheme, which includes the implicit and explicit Euler methods and the Crank–Nicolson scheme. As particular examples we consider scalar quasilinear parabolic PDEs of 2nd order and the time‐dependent incompressible Navier–Stokes equations. © 1998 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 14: 487–518, 1998