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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 analyse residual-based a posteriori error estimates for the virtual element discretisation applied to the thin plate vibration problem in both two and three dimensions. Our approach involves a conforming $C^1$ discrete…
The paper is concerned with parabolic time-periodic boundary value problems which are of theoretical interest and arise in different practical applications. The multiharmonic finite element method is well adapted to this class of parabolic…
We consider in this paper, a new a posteriori residual type error estimator of a conforming mixed finite element method for the coupling of fluid flow with porous media flow on isotropic meshes. Flows are governed by the Navier-Stokes and…
This article initiates the study of space-time adaptive mesh refinements for time-dependent boundary element formulations of wave equations. Based on error indicators of residual type, we formulate an adaptive boundary element procedure for…
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…
An element based adaptation method is developed for an anisotropic a posteriori error estimator. The adaptation does not make use of a metric, but instead equidistributes the error over elements using local mesh modifications. Numerical…
The paper is concerned with the adaptive finite element solution of linear elliptic differential equations using equidistributing meshes. A strategy is developed for defining this type of mesh based on residual-based a posteriori error…
In this paper, a posteriori error estimates of functional type for a stationary diffusion problem with nonsymmetric coefficients are derived. The estimate is guaranteed and does not depend on any particular numerical method. An algorithm…
In this work we derive a posteriori error estimates for the convection-diffusion-reaction equation coupled with the Darcy-Forchheimer problem by a nonlinear external source depending on the concentration of the fluid. We introduce the…
We propose and analyze reliable and efficient a posteriori error estimators for an optimal control problem that involves a nondifferentiable cost functional, the Poisson problem as state equation and control constraints. To approximate the…
We derive functional a posteriori error equalities and constant free two sided estimates for certain types of partial differential equations. The error is measured in a combined norm which takes into account both the primal and dual…
We derive optimal order a posteriori error estimates for fully discrete approximations of the initial-boundary value problem for the heat equation. For the discretization in time we apply the fractional-step $\vartheta$-scheme and for the…
A posteriori error estimates are derived in the context of two-dimensional structural elastic shape optimization under the compliance objective. It is known that the optimal shape features are microstructures that can be constructed using…
We consider finite element methods of multiscale type to approximate solutions for two-dimensional symmetric elliptic partial differential equations with heterogeneous $L^\infty$ coefficients. The methods are of Galerkin type and follow the…
Hybrid quantum/molecular mechanics (QM/MM) models play a pivotal role in molecular simulations. These models provide a balance between accuracy, surpassing pure MM models, and computational efficiency, offering advantages over pure QM…
Reset controllers have demonstrated their effectiveness in enhancing performance in precision motion systems. To further exploiting the potential of reset controllers, this study introduces a parallel-partial reset control structure.…
Sequential Monte Carlo (SMC) methods, also known as particle filters, are simulation-based recursive algorithms for the approximation of the a posteriori probability measures generated by state-space dynamical models. At any given time $t$,…
Atomistic/continuum coupling methods aim to achieve optimal balance between accuracy and efficiency. Adaptivity is the key for the efficient implementation of such methods. In this paper, we carry out a rigorous a posteriori analysis of the…
The purpose of this work is the design and analysis of a reliable and efficient a posteriori error estimator for the so-called pointwise tracking optimal control problem. This linear-quadratic optimal control problem entails the…