Skipping transition conditions ina posteriorierror estimates for finite element discretizations of parabolic equations

Abstract

Abstract. In this paper we derive a posteriori error estimates for the heat equation. The time discretization strategy is based on a θ-method and the mesh used for each time-slab is independent of the mesh used for the previous time-slab. The novelty of this paper is an upper bound for the error caused by the coarsening of the mesh used for computing the solution in the previous time-slab. The technique applied for deriving this upper bound is independent of the problem and can be generalized to other time dependent problems.Mathematics Subject Classification. 65N30, 65N15, 65N50, 65J15.

Space–time adaptive simulations for unsteady Navier–Stokes problems

“…The results of Fig. 19 confirm that at low Reynolds number (Re = 10,20,30,40,50,55) the solution is nearly independent on the mesh; in fact the values of L r =D are overlapped for different space tolerances (Fig. 19).…”

“…In fact any approximation of u ½nÀ1 h on the new space V ½n h introduces an error. In [10] an error indicator bounding this error for the heat equation is proposed. To circumvent this problem we resort to a common refinement mesh X ½nÀ1;n h of the two meshes X ½nÀ1 h and X ½n h .…”

A residual a posteriori error estimate for the Virtual Element Method

“…20,31,27 In recent years a posteriori error analysis and optimality investigations of steady-state adaptive discretizations have been widely tackled for several discretization approaches and model equations, obtaining several interesting results. 32,43,36,26 A large effort has been recently spent on unsteady problems, 47,4,23,37 as well as on other interesting issues like, for example, the analysis of stopping criteria during adaptive iterations. 40 Discretization approaches based on traditional simplicial elements are subject to many constraints when mesh refinement and coarsening are applied.…”

Numerical investigation of effectivity indices of space-time error indicators for Navier–Stokes equations

“…Finally, when we go to the next timestep, the memory allocated by REC is freed. A different approach that skips the requirement of the common refinement Ω h n − 1,n can be found on [7].…”