Related papers: Robust topology optimization using a posteriori er…
Robust topology optimization (RTO), as a class of topology optimization problems, identifies a design with the best average performance while reducing the response sensitivity to input uncertainties, e.g. load uncertainty. Solving RTO is…
We propose and analyze an a posteriori error estimator for a PDE-constrained optimization problem involving a nondifferentiable cost functional, fractional diffusion, and control-constraints. We realize fractional diffusion as the…
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…
In this paper we develop a new a posteriori error analysis for the Monge-Amp\`ere equation approximated by conforming finite element method on isotropic meshes in 2D. The approach utilizes a slight variant of the mixed discretization…
We consider hyperelastic problems and their numerical solution using a conforming finite element discretization and iterative linearization algorithms. For these problems, we present equilibrated, weakly symmetric, $H(\rm{div)}$-conforming…
The area of topology optimization of continuum structures of which is allowed to change in order to improve the performance is now dominated by methods that employ the material distribution concept. The typical methods of the topology…
An integro-differential equation of hyperbolic type, with mixed boundary conditions, is considered. A continuous space-time finite element method of degree one is formulated. A posteriori error representations based on space-time cells is…
This paper is concerned with the analysis and implementation of robust finite element approximation methods for mixed formulations of linear elasticity problems where the elastic solid is almost incompressible. Several novel a posteriori…
For the model problem of the heat equation discretized by an implicit Euler method in time and a conforming finite element method in space, we prove the efficiency of a posteriori error estimators with respect to the energy norm of the…
In this article we consider one-dimensional random systems of hyperbolic conservation laws. We first establish existence and uniqueness of random entropy admissible solutions for initial value problems of conservation laws which involve…
This paper presents an algorithm for reliability-based topology optimization of linear elastic continua under random-field material model. The modelling random field is discretized into a small number of random variables, and then the…
The numerical approximation of convection-dominated problems continues to remain subject of strong interest. Families of stabilization techniques for finite element methods were developed in the past. Adaptive techniques based on a…
In this work we develop and analyze an adaptive finite element method for efficiently solving electrical impedance tomography -- a severely ill-posed nonlinear inverse problem for recovering the conductivity from boundary voltage…
Topology optimization (TO) in two dimensions often presents a trade-off between structural performance and manufacturability, with unpenalized (variable-thickness) methods yielding superior but complex designs, and penalized (SIMP) methods…
In this article, we derive \textit{a posteriori} error estimates for the Dirichlet boundary control problem governed by Stokes equation. An energy-based method has been deployed to solve the Dirichlet boundary control problem. We employ an…
A residual-based a posteriori error estimator is proposed for the incompressible Oseen problem in the convection-dominated regime. The SUPG/PSPG/grad-div stabilized finite element method is used as discretization. The error estimator…
A posteriori error estimates are constructed for the three-field variational formulation of the Biot problem involving the displacements, the total pressure and the fluid pressure. The discretization under focus is the…
An a posteriori error estimator based on an equilibrated flux reconstruction is proposed for defeaturing problems in the context of finite element discretizations. Defeaturing consists in the simplification of a geometry by removing…
In this paper, we study a modified residual-based a posteriori error estimator for the nonconforming linear finite element approximation to the interface problem. The reliability of the estimator is analyzed by a new and direct approach…
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…