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In this paper, we propose a multiphysics finite element method for a nonlinear poroelasticity model. To better describe the processes of deformation and diffusion, we firstly reformulate the nonlinear fluid-solid coupling problem into a…

Numerical Analysis · Mathematics 2021-12-28 Zhihao Ge , Wenlong He

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…

Numerical Analysis · Mathematics 2020-06-09 Xiaobing Feng , Andreas Prohl , Liet Vo

The rigorous convergence analysis of adaptive finite element methods for regularized variational models of quasi-static brittle fracture in strain-limiting elastic solids is presented. This work introduces two novel adaptive mesh refinement…

Numerical Analysis · Mathematics 2025-11-19 Ram Manohar , S. M. Mallikarjunaiah

This paper considers simulation-based optimization of the performance of a regime-switching stochastic system over a finite set of feasible configurations. Inspired by the stochastic fictitious play learning rules in game theory, we propose…

Optimization and Control · Mathematics 2016-11-18 Omid Namvar Gharehshiran , Vikram Krishnamurthy , George Yin

In this paper, we present the periodic modifier-adaptation formulation of the dynamic real time optimization. The proposed formulation uses gradient information to update the problem with affine modifiers so that, upon convergence, its…

Optimization and Control · Mathematics 2023-09-19 Victor Mirasierra , Daniel Limon

This paper presents an innovative optimization framework and algorithm based on the Bayes theorem, featuring adaptive conditioning and jitter. The adaptive conditioning function dynamically modifies the mean objective function in each…

Optimization and Control · Mathematics 2024-01-23 Sarit Maitra

The adaptive nonconforming Morley finite element method (FEM) approximates a regular solution to the von K\'{a}rm\'{a}n equations with optimal convergence rates for sufficiently fine triangulations and small bulk parameter in the D\"orfler…

Numerical Analysis · Mathematics 2020-11-18 Carsten Carstensen , Neela Nataraj

We study a non standard mixed formulation of the Poisson problem, sometimes known as dual mixed formulation. For reasons related to the equilibration of the flux, we use finite elements that are conforming in H(div) for the approximation of…

Numerical Analysis · Mathematics 2022-10-24 Fleurianne Bertrand , Daniele Boffi

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…

Numerical Analysis · Mathematics 2016-10-24 Fernando Gaspoz , Christian Kreuzer , Kunibert Siebert , Daniel Ziegler

A Markov process is registered. At random moment $\theta$ the distribution of observed sequence changes. Using probability maximizing approach the optimal stopping rule for detecting the change is identified. Some explicit solution is…

Probability · Mathematics 2020-11-23 Wojciech Sarnowski , Krzysztof Szajowski

Given n experiment subjects with potentially heterogeneous covariates and two possible treatments, namely active treatment and control, this paper addresses the fundamental question of determining the optimal accuracy in estimating the…

Machine Learning · Statistics 2024-11-13 Jiachun Li , David Simchi-Levi , Yunxiao Zhao

This paper focuses on the quasi-optimality of an adaptive nonconforming finite element method for a distributed optimal control problem governed by the Stokes equation. The nonconforming lowest order Crouzeix-Raviart element and piecewise…

Numerical Analysis · Mathematics 2026-03-24 Tooba M. Shaikh , Asha K. Dond

We consider the standard adaptive finite element loop SOLVE, ESTIMATE, MARK, REFINE, with ESTIMATE being implemented using the $p$-robust equilibrated flux estimator, and MARK being D\"orfler marking. As a refinement strategy we employ…

Numerical Analysis · Mathematics 2016-11-15 Claudio Canuto , Ricardo H. Nochetto , Rob Stevenson , Marco Verani

This paper presents and analyzes an immersed finite element (IFE) method for solving Stokes interface problems with a piecewise constant viscosity coefficient that has a jump across the interface. In the method, the triangulation does not…

Numerical Analysis · Mathematics 2025-07-24 Haifeng Ji , Feng Wang , Jinru Chen , Zhilin Li

In this paper, we study an adaptive finite element method for multiple eigenvalue problems of a class of second order elliptic equations. By using some eigenspace approximation technology and its crucial property which is also presented in…

Numerical Analysis · Mathematics 2013-09-18 Xiaoying Dai , Lianhua He , Aihui Zhou

In this paper, we propose an extended mixed finite element method for elliptic interface problems. By adding some stabilization terms, we present a mixed approximation form based on Brezzi-Douglas-Marini element space and the piecewise…

Numerical Analysis · Mathematics 2022-03-14 Pei Cao , Jinru Chen , Feng Wang

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…

Numerical Analysis · Mathematics 2018-10-08 Alejandro Allendes , Francisco Fuica , Enrique Otárola , Daniel Quero

This paper derives a posteriori error estimators for the nonlinear first-order optimality conditions associated with the electrically and flexoelectrically coupled Frank-Oseen model of liquid crystals, building on the results of [14] for…

Numerical Analysis · Mathematics 2018-06-19 D. B. Emerson

This paper is interested in the problem of optimal stopping in a mean field game context. The notion of mixed solution is introduced to solve the system of partial differential equations which models this kind of problem. This notion…

Analysis of PDEs · Mathematics 2017-06-14 C. Bertucci

We propose a new method to design adaptation algorithms that guarantee a certain prescribed level of performance and are applicable to systems with nonconvex parameterization. The main idea behind the method is, given the desired…

Optimization and Control · Mathematics 2007-05-23 I. Y. Tyukin , D. V. Prokhorov , Cees van Leeuwen