A posteriori error estimates for nonlinear problems: Lr, (0, T; W1,ρ (Ω))-error estimates for finite element discretizations of parabolic equations

✍ Scribed by R. Verfürth

• Publisher: John Wiley and Sons
• Year: 1998
• Tongue: English
• Weight: 546 KB
• Volume: 14
• Category: Article
• ISSN: 0749-159X
• DOI: 10.1002/(sici)1098-2426(199807)14:4<487::aid-num4>3.0.co;2-g

✦ Synopsis

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.