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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…

Numerical Analysis · Mathematics 2026-04-28 Muhammad Afzal , Naveed Ahmed , Volker John

In this study, we employ the variational multiscale (VMS) concept to develop a posteriori error estimates for the stationary convection-diffusion-reaction equation. The variational multiscale method is based on splitting the continuous part…

Numerical Analysis · Mathematics 2025-05-06 Ramon Codina , Hauke Gravenkamp , Sheraz Ahmed Khan

In this paper, we study an optimal boundary control problem for the Boussinesq equations, which couple the time-dependent Navier-Stokes system with a heat equation, where the control enters through a Robin boundary condition on temperature.…

Numerical Analysis · Mathematics 2026-03-03 Wei Gong , Dongdong Liang , Xianbing Luo , Changlun Ye

This paper develops a general methodology for a posteriori error estimation in time-dependent multiphysics numerical simulations. The methodology builds upon the generalized-structure additive Runge--Kutta (GARK) approach to time…

Numerical Analysis · Mathematics 2020-01-27 Mahesh Narayanamurthi , Ulrich Römer , Adrian Sandu

We present new aposteriori error estimates for the interior penalty discontinuous Galerkin method applied to non-stationary convection-diffusion equations. The focus is on strongly convection-dominated problems without zeroth-order reaction…

Numerical Analysis · Mathematics 2025-04-14 Tiffany Barry , Andrea Cangiani , Samuel P. Cox , Emmanuil H. Georgoulis

Defeaturing, the process of simplifying computational geometries, is a critical step in industrial simulation pipelines for reducing computational cost. Rigorous a posteriori estimators exist for the global energy-norm error introduced by…

Numerical Analysis · Mathematics 2025-12-24 Philipp Weder , Annalisa Buffa

Motivated by an energy efficient building application, we want to optimize a quadratic cost functional subject to the Boussinesq approximation of the Navier-Stokes equations and to bilateral state and control constraints. Since the…

Optimization and Control · Mathematics 2021-01-13 Julian Andrej , Lars Grüne , Luca Mechelli , Thomas Meurer , Simon Pirkelmann , Stefan Volkwein

Deep learning has shown successful application in visual recognition and certain artificial intelligence tasks. Deep learning is also considered as a powerful tool with high flexibility to approximate functions. In the present work,…

Machine Learning · Computer Science 2021-12-23 Ayan Chakraborty , Thomas Wick , Xiaoying Zhuang , Timon Rabczuk

The present paper is dedicated to the global well-posedness issue for the Boussinesq system with the temperature-dependent viscosity in $\mathbb{R}^2.$ We aim at extending the work by Abidi and Zhang ( Adv. Math. 2017 (305) 1202--1249 ) to…

Analysis of PDEs · Mathematics 2017-06-27 Xiaoping Zhai , Boqing Dong , Zhimin Chen

Global well-posedness of strong solutions and existence of the global attractor to the initial and boundary value problem of 2D Boussinesq system in a periodic channel with non-homogeneous boundary conditions for the temperature and…

Analysis of PDEs · Mathematics 2014-03-07 Aimin Huang

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…

Numerical Analysis · Mathematics 2017-03-07 Koffi Wilfrid Houedanou , Jamal Adetola , Bernardin Ahounou

We study temperature and velocity output tracking problem for a two-dimensional room model with the fluid dynamics governed by the linearized translated Boussinesq equations. Additionally, the room model includes finite-dimensional models…

Optimization and Control · Mathematics 2023-03-01 Konsta Huhtala , Lassi Paunonen , Weiwei Hu

In this paper we obtain a result about the global existence of weak solutions for the $d$-dimensional Bussinesq system, with viscosity dependent on temperature. The initial temperature is just supposed to be bounded, while the initial…

Analysis of PDEs · Mathematics 2015-11-03 Francesco De Anna

A parametric instability of an incompressible, viscous, and Boussinesq fluid layer bounded between two parallel planes is investigated numerically. The layer is assumed to be inclined at an angle with horizontal. The planes bounding the…

Fluid Dynamics · Physics 2023-05-01 Jitender Singh

Simulated tempering is popular method of allowing MCMC algorithms to move between modes of a multimodal target density {\pi}. One problem with simulated tempering for multimodal targets is that the weights of the various modes change for…

Computation · Statistics 2019-02-12 Nicholas G. Tawn , Gareth O. Roberts , Jeffrey S. Rosenthal

We present a robust and efficient target-based mesh adaptation methodology, building on hybridized discontinuous Galerkin schemes for (nonlinear) convection-diffusion problems, including the compressible Euler and Navier-Stokes equations.…

Numerical Analysis · Mathematics 2014-11-12 Michael Woopen , Georg May , Jochen Schütz

Port-Hamiltonian systems provide an energy-based modeling paradigm for dynamical input-state-output systems. At their core, they fulfill an energy balance relating stored, dissipated and supplied energy. To accurately resolve this energy…

Numerical Analysis · Mathematics 2024-12-17 Andreas Bartel , Manuel Schaller

Bayesian methods feature useful properties for solving inverse problems, such as tomographic reconstruction. The prior distribution introduces regularization, which helps solving the ill-posed problem and reduces overfitting. In practice,…

Image and Video Processing · Electrical Eng. & Systems 2021-12-02 Max-Heinrich Laves , Malte Tölle , Alexander Schlaefer , Sandy Engelhardt

This paper is concerned with goal-oriented a posteriori error estimation for nonlinear functionals in the context of nonlinear variational problems solved with continuous Galerkin finite element discretizations. A two-level, or discrete,…

Computational Engineering, Finance, and Science · Computer Science 2025-01-10 Brian N. Granzow , D. Thomas Seidl , Stephen D. Bond

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…

Numerical Analysis · Mathematics 2011-08-24 Qingshan Chen , Max Gunzburger