Goal-Oriented Error Estimation for the Fractional Step Theta Scheme

Goal-Oriented Error Estimation for the Fractional Step Theta Scheme

In this work, we derive a goal-oriented a posteriori error estimator for the error due to time-discretization of nonlinear parabolic partial differential equations by the fractional step theta method. This time-stepping scheme is assembled by three steps of the general theta method, that also unifies simple schemes like forward and backward Euler as well as the Crank–Nicolson method. Further, b...

A Posteriori Error Estimation for the Fractional Step Theta Discretization of the Incompressible Navier-Stokes Equations

In this work, we derive a goal-oriented a posteriori error estimator for the error due to time discretization. As time discretization scheme we consider the fractional step theta method, that consists of three subsequent steps of the one-step theta method. In every sub-step, the full incompressible system has to be solved (in contrast to time integrators of operator splitting type). The resulti...

Goal - Oriented Error Estimation and Adaptivity for theFinite Element

In this paper, we study a new approach in a posteriori error estimation, in which the numerical error of nite element approximations is estimated in terms of quantities of interest rather than the classical energy norm. These so-called quantities of interest are characterized by linear functionals on the space of functions to where the solution belongs. We present here the theory with respect t...

Goal-oriented error estimation for fast approximations of nonlinear problems

A Posteriori Error Estimates for the Fractional–step Θ-scheme for Linear Parabolic Equations

We derive residual-based a posteriori error estimates of optimal order for time discretizations by the fractional-step θ-scheme for linear parabolic equations. First, we consider the time semi-discrete problem. The main tool of our analysis is an appropriate reconstruction of the piecewise linear interpolant of the approximate solution that leads to a residual of optimal order. Next, we extend ...