Related papers: Error estimation and adaptive moment hierarchies f…

In this article, goal-oriented a posteriori error estimation for the biharmonic plate bending problem is considered. The error for approximation of goal functional is represented by an estimator which combines dual-weighted residual method…

This paper presents a numerical approximation technique for the Boltzmann equation based on a moment system approximation in velocity dependence and a discontinuous Galerkin finite-element approximation in position dependence. The closure…

We use the ideas of goal-oriented error estimation and adaptivity to design and implement an efficient adaptive algorithm for approximating linear quantities of interest derived from solutions to elliptic partial differential equations…

This work is devoted to the study of a posteriori error estimation and adaptivity in parabolic problems with a particular focus on spatial discontinuous Galerkin (dG) discretisations. We begin by deriving an a posteriori error estimator for…

This work reviews goal-oriented a posteriori error control, adaptivity and solver control for finite element approximations to boundary and initial-boundary value problems for stationary and non-stationary partial differential equations,…

This paper is concerned with the numerical approximation of quantities of interest associated with solutions to parametric elliptic partial differential equations (PDEs). The key novelty of this work is in its focus on the quantities of…

This work is concerned with the derivation of a robust a posteriori error estimator for a discontinuous Galerkin method discretisation of linear non-stationary convection-diffusion initial/boundary value problems and with the implementation…

We consider a linear elliptic partial differential equation (PDE) with a generic uniformly bounded parametric coefficient. The solution to this PDE problem is approximated in the framework of stochastic Galerkin finite element methods. We…

This paper is concerned with goal-oriented a posteriori error estimation for nonlinear functionals in the context of nonlinear variational problems solved with continuous Galerkin finite element discretizations. A two-level, or discrete,…

We derive a fully computable aposteriori error estimator for a Galerkin finite element solution of the wave equation with explicit leapfrog time-stepping. Our discrete formulation accommodates both time evolving meshes and leapfrog based…

This work is concerned with the derivation of an a posteriori error estimator for Galerkin approximations to nonlinear initial value problems with an emphasis on finite-time existence in the context of blow-up. The stucture of the derived…

We propose and analyze novel adaptive algorithms for the numerical solution of elliptic partial differential equations with parametric uncertainty. Four different marking strategies are employed for refinement of stochastic Galerkin finite…

This paper analyses discontinuous Galerkin finite element methods (DGFEM) to approximate a regular solution to the von K\'arm\'an equations defined on a polygonal domain. A discrete inf-sup condition sufficient for the stability of the…

This work is concerned with the development of an adaptive numerical method for semilinear heat flow models featuring a general (possibly) nonlinear reaction term that may cause the solution to blow up in finite time. The fully discrete…

We propose a goal-oriented mesh-adaptive algorithm for a finite element method stabilized via residual minimization on dual discontinuous-Galerkin norms. By solving a saddle-point problem, this residual minimization delivers a stable…

This work is concerned with the development of a space-time adaptive numerical method, based on a rigorous a posteriori error bound, for a semilinear convection-diffusion problem which may exhibit blow-up in finite time. More specifically,…

We propose and analyze a general goal-oriented adaptive strategy for approximating quantities of interest (QoIs) associated with solutions to linear elliptic partial differential equations with random inputs. The QoIs are represented by…

We present new aposteriori error estimates for the interior penalty discontinuous Galerkin method applied to non-stationary convection-diffusion equations. The focus is on strongly convection-dominated problems without zeroth-order reaction…

We deal with the numerical solution of the compressible Euler equations with the aid of the discontinuous Galerkin (DG) method with focus on the goal-oriented error estimates and adaptivity. We analyze the adjoint consistency of the DG…

The paper considers a class of parametric elliptic partial differential equations (PDEs), where the coefficients and the right-hand side function depend on infinitely many (uncertain) parameters. We introduce a two-level a posteriori…