Goal-oriented error estimation for fluid–structure interaction problems

Goal-oriented error estimation for fast approximations of nonlinear problems

Goal-oriented a posteriori error estimates for transport problems

Some aspects of goal-oriented a posteriori error estimation are addressed in the context of steady convection-diffusion equations. The difference between the exact and approximate values of a linear target functional is expressed in terms of integrals that depend on the solutions to the primal and dual problems. Gradient averaging techniques are employed to separate the element residual and dif...

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 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...

Toward alternative bounding techniques for robust goal-oriented error estimation applied to linear problems

In this work, we propose appealing bounding techniques that enable to derive accurate and strict error bounds on outputs of interest computed from numerical approximation methods such as the finite element method. These techniques are based on Saint-Venant’s principle and exploit specific homotheticity properties in order to improve the quality of the bounds computed from the classical bounding...