Related papers: A posteriori error estimation and adaptive strateg…
We propose and analyze a posteriori error estimators for an optimal control problem that involves an elliptic partial differential equation as state equation and a control variable that enters the state equation as a coefficient; pointwise…
The a posteriori analysis of the discretization error and the modeling error is studied for a compliance cost functional in the context of the optimization of composite elastic materials and a two-scale linearized elasticity model. A…
We consider fully discrete time-space approximations of abstract linear parabolic partial differential equations (PDEs) consisting of an $hp$-version discontinuous Galerkin (DG) time stepping scheme in conjunction with standard (conforming)…
We derive globally reliable a posteriori error estimators for a PDE-constrained optimization problem involving linear models in fluid dynamics as state equation; control constraints are also considered. The corresponding local error…
In this work, we propose to efficiently solve time dependent parametrized optimal control problems governed by parabolic partial differential equations through the certified reduced basis method. In particular, we will exploit an error…
In this paper we present an algorithm for adaptive sparse grid approximations of quantities of interest computed from discretized partial differential equations. We use adjoint-based a posteriori error estimates of the physical…
A posteriori error estimators are studied for discontinuous Galerkin methods for solving a frictional contact problem, which is a representative elliptic variational inequality of the second kind. The estimators are derived by relating the…
A posteriori estimates give bounds on the error between the unknown solution of a partial differential equation and its numerical approximation. We present here the methodology based on H1-conforming potential and H(div)-conforming…
Inverse problems use physical measurements along with a computational model to estimate the parameters or state of a system of interest. Errors in measurements and uncertainties in the computational model lead to inaccurate estimates. This…
We consider the a posteriori error analysis of fully discrete approximations of parabolic problems based on conforming $hp$-finite element methods in space and an arbitrary order discontinuous Galerkin method in time. Using an equilibrated…
We propose and analyze a reliable and efficient a posteriori error estimator for a constrained linear-quadratic optimal control problem involving Dirac measures; the control variable corresponds to the amplitude of forces modeled as point…
Motivated by problems in contact mechanics, we propose a duality approach for computing approximations and associated a posteriori error bounds to solutions of variational inequalities of the first kind. The proposed approach improves upon…
We present a new residual-type energy-norm a posteriori error analysis for interior penalty discontinuous Galerkin (dG) methods for linear elliptic problems. The new error bounds are also applicable to dG methods on meshes consisting of…
We establish rigorous \emph{a posteriori} error bounds for a space-time finite element method of arbitrary order discretising linear wave problems in second order formulation. The method combines standard finite elements in space and…
This study presents an aposteriori error analysis of adaptive finite element approximations of parabolic boundary control problems with bilateral box constraints that act on a Neumann boundary. The control problem is discretized using the…
We derive aposteriori error estimates for fully discrete approximations to solutions of linear parabolic equations on the space-time domain. The space discretization uses finite element spaces, that are allowed to change in time. Our main…
Accurate error estimation is crucial in model order reduction, both to obtain small reduced-order models and to certify their accuracy when deployed in downstream applications such as digital twins. In existing a posteriori error estimation…
We consider a 1D periodic atomistic model, for which we formulate and analyze an adaptive variant of a quasicontinuum method. We establish a posteriori error estimates for the energy norm and for the energy, based on a posteriori residual…
We consider finite element solutions to optimization problems, where the state depends on the possibly constrained control through a linear partial differential equation. Basing upon a reduced and rescaled optimality system, we derive a…
In this article, a posteriori error analysis is developed for mixed finite element Galerkin approximations to a second order linear hyperbolic equation. Based on mixed elliptic reconstructions and an integration tool, which is a variation…