Related papers: Mesh adaptivity driven by goal-oriented locally eq…
The recovery type error estimators introduced by Zienkiewicz and Zhu use a recovered stress field evaluated from the Finite Element (FE) solution. Their accuracy depends on the quality of the recovered field. In this sense, accurate results…
Goal oriented error estimation and adaptive procedures are essential for the accurate and efficient evaluation of numerical simulations that involve complex domains. By locally improving the approximation quality we can solve expensive…
Given a partial differential equation (PDE), goal-oriented error estimation allows us to understand how errors in a diagnostic quantity of interest (QoI), or goal, occur and accumulate in a numerical approximation, for example using the…
Purpose: This paper aims at assessing the effect of (1) the statical admissibility of the recovered solution; (2) the ability of the recovered solution to represent the singular solution; on the accuracy, local and global effectivity of…
In this paper a new technique aimed to obtain accurate estimates of the error in energy norm using a moving least squares (MLS) recovery-based procedure is presented. We explore the capabilities of a recovery technique based on an enhanced…
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…
Superconvergence and a posteriori error estimators of recovery type are analyzed for the 4-node hybrid stress quadrilateral finite element method proposed by Pian and Sumihara (Int. J. Numer. Meth. Engrg., 1984, 20: 1685-1695) for linear…
In this work, we consider adaptive mesh refinement for a monolithic phase-field description for fractures in brittle materials. Our approach is based on an a posteriori error estimator for the phase-field variational inequality realizing…
An error control technique aimed to assess the quality of smoothed finite element approximations is presented in this paper. Finite element techniques based on strain smoothing appeared in 2007 were shown to provide significant advantages…
This paper introduces an explicit residual-based a posteriori error analysis for the symmetric mixed finite element method in linear elasticity after Arnold-Winther with pointwise symmetric and H(div)-conforming stress approximation.…
Quantitative Susceptibility Mapping is a parametric imaging technique to estimate the magnetic susceptibilities of biological tissues from MRI phase measurements. This problem of estimating the susceptibility map is ill posed. Regularized…
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…
Pixel- and voxel-based representations of microstructures obtained from tomographic imaging methods is an established standard in computational materials science. The corresponding highly resolved, uniform discretitization in numerical…
Adaptive quasicontinuum (QC) methods are important methodologies in molecular mechanics for the simulations of materials with defects, intending to achieve the optimal balance of accuracy and efficiency on the fly. In this study, we propose…
In this paper we develop two goal-oriented adaptive strategies for a posteriori error estimation within the generalized multiscale finite element framework. In this methodology, one seeks to determine the number of multiscale basis…
We propose a new heuristic goal-oriented a posteriori error estimator that connects the dual weighted residual method with equilibrated a posteriori error estimation. Our numerical experiments demonstrate the practical reliability of the…
The $\xi$-based spatially adaptive three-field variable phase-field model for quasi-static anti-plane crack propagation is introduced. A dynamically optimized regularization length is integrated to improve computational efficiency and…
The convergence analysis for least-squares finite element methods led to various adaptive mesh-refinement strategies: Collective marking algorithms driven by the built-in a posteriori error estimator or an alternative explicit…
We present a priori and superconvergence error estimates of mixed finite element methods for the pseudostress-velocity formulation of the Oseen equation. In particular, we derive superconvergence estimates for the velocity and a priori…
We introduce a goal-oriented strategy for multiscale computations performed using the Multiscale Finite Element Method (MsFEM). In a previous work, we have shown how to use, in the MsFEM framework, the concept of Constitutive Relation Error…