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We develop a structure-preserving computational framework for optimal mixing control in incompressible flows. Our approach exactly conserves the continuous system's key invariants (mass and $L^2$-energy), while also maintaining discrete…

Numerical Analysis · Mathematics 2026-01-13 Weiwei Hu , Ziqian Li , Yubiao Zhang , Enrique Zuazua

In this paper, we present a novel solution strategy for the Cahn-Hilliard-Biot model, a three-way coupled system that features the interplay of solid phase separation, fluid dynamics, and elastic deformations in porous media. It is a…

Numerical Analysis · Mathematics 2026-02-02 Cedric Riethmüller , Erlend Storvik

We propose a novel decoupled unconditionally stable numerical scheme for the simulation of two-phase flow in a Hele-Shaw cell which is governed by the Cahn-Hilliard-Hele-Shaw system (CHHS) with variable viscosity. The temporal…

Numerical Analysis · Mathematics 2014-11-03 Daozhi Han

In this paper, we consider a non-linear fourth-order evolution equation of Cahn-Hilliard-type on evolving surfaces with prescribed velocity, where the non-linear terms are only assumed to have locally Lipschitz derivatives. High-order…

Numerical Analysis · Mathematics 2022-03-07 Cedric Aaron Beschle , Balázs Kovács

We present high-order variational Lagrangian finite element methods for compressible fluids using a discrete energetic variational approach. Our spatial discretization is mass/momentum/energy conserving and entropy stable. Fully implicit…

Numerical Analysis · Mathematics 2023-08-16 Guosheng Fu , Chun Liu

In the present work, a new computational framework for structural topology optimization based on the concept of moving deformable components is proposed. Compared with the traditional pixel or node point-based solution framework, the…

Computational Engineering, Finance, and Science · Computer Science 2015-06-23 Xu Guo , Weisheng Zhang , Wenliang Zhong

This paper develops a sliding mode control based frame work for equality constrained optimization by reformulation the first order Karush Kuhn Tucker conditions as control affine dynamical system. The optimization variables are treated as…

Optimization and Control · Mathematics 2026-05-01 Shyam Kamal , Baby Diana , Sunidhi Pandey , Sandip Ghosh , Thach Ngoc Dinh

We reconsider the variational integration of optimal control problems for mechanical systems based on a direct discretization of the Lagrange-d'Alembert principle. This approach yields discrete dynamical constraints which by construction…

Optimization and Control · Mathematics 2012-04-30 C. M. Campos , O. Junge , S. Ober-Blöbaum

We propose a fluid-based topology optimization methodology for convective heat-transfer problems that can manage an extensive number of design variables, enabling the fine geometric features required for the next generation of…

The Cahn--Hilliard equation is a widely used model that describes amongst others phase separation processes of binary mixtures or two-phase flows. In the recent years, different types of boundary conditions for the Cahn--Hilliard equation…

Numerical Analysis · Mathematics 2021-03-04 Stefan Metzger

We propose an efficient threshold dynamics method for topology optimization for fluids modeled with the Stokes equation. The proposed algorithm is based on minimization of an objective energy function that consists of the dissipation power…

Optimization and Control · Mathematics 2018-12-27 Huangxin Chen , Haitao Leng , Dong Wang , Xiao-Ping Wang

Topology optimization is concerned with the identification of optimal shapes of deformable bodies with respect to given target functionals. The focus of this paper is on a topology optimization problem for a time-evolving elastoplastic…

Analysis of PDEs · Mathematics 2021-06-21 Stefano Almi , Ulisse Stefanelli

We study some optimal control problems associated to the evolution of two isothermal, incompressible, immisible fluids in a two-dimensional bounded domain. The Cahn- Hilliard-Navier-Stokes model consists of a Navier-Stokes equation…

Analysis of PDEs · Mathematics 2019-03-20 Tania Biswas , Sheetal Dharmatti , Manil T Mohan

We introduce a numerical variational method based on the Rayleigh-Ritz optimization principle for predicting two-dimensional self-trapped beams in nonlinear media. This technique overcomes the limitation of the traditional variational…

Optics · Physics 2018-04-04 Erick I. Duque , Servando Lopez-Aguayo , Boris A. Malomed

We consider numerical solution of elliptic problems with heterogeneous diffusion coefficients containing thin highly conductive structures. Such problems arise e.g. in fractured porous media, reinforced materials, and electric circuits. The…

Numerical Analysis · Mathematics 2020-07-22 Fredrik Hellman , Axel Målqvist , Siyang Wang

The Cahn-Hilliard equation is a fundamental model for describing phase separation phenomena in binary mixtures. Traditional numerical methods, such as finite difference and finite element methods, often incur substantial computational cost,…

Numerical Analysis · Mathematics 2026-05-26 Yi Liu , Shuting Gu

This article presents a new finite element method for convection-diffusion equations by enhancing the continuous finite element space with a flux space for flux approximations that preserve the important mass conservation locally on each…

Numerical Analysis · Mathematics 2017-10-24 Yujie Liu , Junping Wang , Qingsong Zou

In this article, we are concerned with the analysis on the numerical reconstruction of the spatial component in the source term of a time-fractional diffusion equation. This ill-posed problem is solved through a stabilized nonlinear…

Numerical Analysis · Mathematics 2020-05-06 Daijun Jiang , Yikan Liu , Dongling Wang

Permitting multiple materials within a topology optimization setting increases the search space of the technique, which facilitates obtaining high-performing and efficient optimized designs. Structures with multiple materials involving…

Computational Engineering, Finance, and Science · Computer Science 2023-05-16 Prabhat kumar

The Cahn-Hilliard equation and extensions, notably the Cahn-Hilliard-Darcy and Cahn-Hilliard-Navier-Stokes systems, provide widely used frameworks for coupling interfacial thermodynamics with flow. This review surveys the thermodynamic…

Numerical Analysis · Mathematics 2026-02-10 Aaron Brunk , Marco F. P. ten Eikelder , Marvin Fritz , Dennis Höhn , Dennis Trautwein