Related papers: Goal-oriented Atomistic-Continuum Adaptivity for t…
The spectral deferred correction method is a variant of the deferred correction method for solving ordinary differential equations. A benefit of this method is that is uses low order schemes iteratively to produce a high order…
In this work, we apply multi-goal oriented error estimation to the finite element method. In particular, we use the dual weighted residual method and apply it to a model problem. This model problem consist of locally different coercive…
We shall develop a fully discrete space-time adaptive method for linear parabolic problems based on new reliable and efficient a posteriori analysis for higher order dG(s) finite element discretisations. The adaptive strategy is motivated…
In this article we develop convergence theory for a class of goal-oriented adaptive finite element algorithms for second order nonsymmetric linear elliptic equations. In particular, we establish contraction results for a method of this type…
In this paper, we study the adaptive planewave discretization for a cluster of eigenvalues of second-order elliptic partial differential equations. We first design an a posteriori error estimator and prove both the upper and lower bounds.…
We derive efficient and reliable goal-oriented error estimations, and devise adaptive mesh procedures for the finite element method that are based on the localization of a posteriori estimates. In our previous work [SIAM J. Sci. Comput.,…
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…
Motivated by the desire to numerically calculate rigorous upper and lower bounds on deviation probabilities over large classes of probability distributions, we present an adaptive algorithm for the reconstruction of increasing real-valued…
Frequency-limited model order reduction aims to approximate a high-order model with a reduced-order model that maintains high fidelity within a specific frequency range. Beyond this range, a decrease in accuracy is acceptable due to the…
Large-scale linear, time-invariant (LTI) dynamical systems are widely used to characterize complicated physical phenomena. We propose a two-stage algorithm to reduce the order of a large-scale LTI system given samples of its transfer…
Automatic algorithms attempt to provide approximate solutions that differ from exact solutions by no more than a user-specified error tolerance. This paper describes an automatic, adaptive algorithm for approximating the solution to a…
We consider initial value problems where we are interested in a quantity of interest (QoI) that is the integral in time of a functional of the solution of the IVP. For these, we look into local error based time adaptivity. We derive a goal…
In this paper, we present an adaptive framework for constructing a pseudo-optimal reduced model for the frequency-limited H2-optimal model order reduction problem. We show that the frequency-limited pseudo-optimal reduced-order model has an…
We propose and analyze a reliable and efficient a posteriori error estimator for the pointwise tracking optimal control problem of the Stokes equations. This linear-quadratic optimal control problem entails the minimization of a cost…
Mixed atomistic and continuum methods offer the possibility of carrying out simulations of material properties at both larger length scales and longer times than direct atomistic calculations. The quasi-continuum method links atomistic and…
We provide a posteriori error estimates for a discontinuous Galerkin scheme for the parabolic-elliptic Keller-Segel system in 2 or 3 space dimensions. The estimates are conditional, in the sense that an a posteriori computable quantity…
In this paper, we introduce a novel a posteriori error estimator for the conforming finite element approximation to the H(curl) problem with inhomogeneous media and with the right-hand side only in L^2. The estimator is of the recovery…
In this work, we develop adaptive schemes using goal-oriented error control for a highly nonlinear flow temperature model with temperature dependent density. The dual-weighted residual method for computing error indicators to steer mesh…
We consider some (anisotropic and piecewise constant) convection-diffusion-reaction problems in domains of R2, approximated by a discontinuous Galerkin method with polynomials of any degree. We propose two a posteriori error estimators…
This article is a review on basic concepts and tools devoted to a posteriori error estimation for problems solved with the Finite Element Method. For the sake of simplicity and clarity, we mostly focus on linear elliptic diffusion problems,…