Related papers: Solution Techniques for the Stokes System: A prior…
In this paper, we present a new multiscale model reduction technique for the Stokes flows in heterogeneous perforated domains. The challenge in the numerical simulations of this problem lies in the fact that the solution contains many…
We introduce and analyze a post-processing for a family of variational space-time approximations to wave problems. The discretization in space and time is based on continuous finite element methods. The post-processing lifts the fully…
We investigate several robust preconditioners for solving the saddle-point linear systems that arise from spatial discretization of unsteady and steady variable-coefficient Stokes equations on a uniform staggered grid. Building on the…
Based on the Uzawa algorithm, we consider an adaptive finite element method for the Stokes system. We prove linear convergence with optimal algebraic rates for the residual estimator (which is equivalent to the total error), if the arising…
Piecewise divergence-free nonconforming virtual elements are designed for Stokes problem in any dimensions. After introducing a local energy projector based on the Stokes problem and the stabilization, a divergence-free nonconforming…
In our work, we consider the classical density-based approach to topology optimization. We propose the modification of the discretized cost/objective functional using a posteriori error estimator for the finite element method. It can be…
The paper studies a higher order unfitted finite element method for the Stokes system posed on a surface in three-dimensional space. The method employs generalized Taylor-Hood finite element pairs on tetrahedral bulk mesh to discretize the…
This paper concerns models and convergence principles for dealing with stochasticity in a wide range of algorithms arising in nonlinear analysis and optimization in Hilbert spaces. It proposes a flexible geometric framework within which…
A general framework for goal-oriented a posteriori error estimation for finite volume methods is presented. The framework does not rely on recasting finite volume methods as special cases of finite element methods, but instead directly…
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…
We derive a residual-based a posteriori error estimator for the conforming hp-Adaptive Finite Element Method (hp-AFEM) for the steady state Stokes problem describing the slow motion of an incompressible fluid. This error estimator is…
An algorithm is proposed for solving optimization problems arising in neural network training for supervised learning. The unique feature of the algorithm is the use of an auxiliary loss, in addition to the original loss employed for model…
We propose some new mixed finite element methods for the time dependent stochastic Stokes equations with multiplicative noise, which use the Helmholtz decomposition of the driving multiplicative noise. It is known [16] that the pressure…
We develop a high order cut finite element method for the Stokes problem based on general inf-sup stable finite element spaces. We focus in particular on composite meshes consisting of one mesh that overlaps another. The method is based on…
We develop $H$(div)-conforming mixed finite element methods for the unsteady Stokes equations modeling single-phase incompressible fluid flow. A projection method in the framework of the incremental pressure correction methodology is…
Accelerated proximal gradient methods have recently been developed for solving quasi-static incremental problems of elastoplastic analysis with some different yield criteria. It has been demonstrated through numerical experiments that these…
We present a strategy for solving time-dependent problems on grids with local refinements in time using different time steps in different regions of space. We discuss and analyze two conservative approximations based on finite volume with…
Stochastic restoration algorithms allow to explore the space of solutions that correspond to the degraded input. In this paper we reveal additional fundamental advantages of stochastic methods over deterministic ones, which further motivate…
We consider large linear and nonlinear fixed point problems, and solution with proximal algorithms. We show that there is a close connection between two seemingly different types of methods from distinct fields: 1) Proximal iterations for…
We provide a novel computer-assisted technique for systematically analyzing first-order methods for optimization. In contrast with previous works, the approach is particularly suited for handling sublinear convergence rates and stochastic…