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In this work, we design and analyze a novel, provably conditionally stable, weakly coupled partitioned scheme to solve the conjugate heat transfer (CHT) problem. We consider a model CHT problem consisting of linear advection-diffusion and…

Numerical Analysis · Mathematics 2026-02-23 Sarah Nataj , David C. Del Rey Fernández , David Brown , Rajeev Jaiman

In this work, we propose an accurate, robust, and stable discretization of the gamma-based compressible multicomponent model by Shyue [J. Comput. Phys., 142 (1998), 208-242] where each component follows a stiffened gas equation of state…

Numerical Analysis · Mathematics 2025-10-10 Rémi Abgrall , Pratik Rai , Florent Renac

We construct a structure-preserving finite element method and time-stepping scheme for inhomogeneous, incompressible magnetohydrodynamics (MHD). The method preserves energy, cross-helicity (when the fluid density is constant), magnetic…

Numerical Analysis · Mathematics 2020-12-09 Evan S. Gawlik , François Gay-Balmaz

We present and analyze a new derivation of the meso-level behavior of a discrete microscopic model of heat transfer. This construction is based on the principle of dynamic consistency. Our work reproduces and corrects, when needed, all the…

Dynamical Systems · Mathematics 2023-01-18 Ronald E. Mickens , Talitha Washington

In this paper, we review and systematically compare three finite element discretization methods for a harmonic map heat flow problem from the unit disk in $\mathbb{R}^2$ to the unit sphere in $\mathbb{R}^3$ in an unified framework.…

Numerical Analysis · Mathematics 2025-08-29 Nam Anh Nguyen , Arnold Reusken

In this paper, we present a novel second order in time mixed finite element scheme for the Cahn-Hilliard-Navier-Stokes equations with matched densities. The scheme combines a standard second order Crank-Nicholson method for the…

Numerical Analysis · Mathematics 2016-06-09 Amanda E. Diegel , Cheng Wang , Xiaoming Wang , Steven M. Wise

We consider data assimilation for the heat equation using a finite element space semi-discretization. The approach is optimization based, but the design of regularization operators and parameters rely on techniques from the theory of…

Numerical Analysis · Mathematics 2016-09-19 Erik Burman , Lauri Oksanen

This paper presents a nonlinear reaction-diffusion-fluid system that simulates radiofrequency ablation within cardiac tissue. The model conveys the dynamic evolution of temperature and electric potential in both the fluid and solid regions,…

Numerical Analysis · Mathematics 2024-05-03 Mostafa Bendahmane , Youssef Ouakrim , Yassine Ouzrour , Mohamed Zagour

We present a numerical investigation of stochastic transport in ideal fluids. According to Holm (Proc Roy Soc, 2015) and Cotter et al. (2017), the principles of transformation theory and multi-time homogenisation, respectively, imply a…

Fluid Dynamics · Physics 2018-09-28 Colin J. Cotter , Dan Crisan , Darryl D. Holm , Wei Pan , Igor Shevchenko

In this work, we present a comprehensive theoretical analysis for Virtual Element discretizations of incompressible non-Newtonian flows governed by the Carreau-Yasuda constitutive law, in the shear-thickening regime (r > 2) including both…

We consider numerical simulation of the isotropic elastic wave equations arising from seismic applications with non-trivial land topography. The more flexible finite element method is applied to the shallow region of the simulation domain…

Numerical Analysis · Mathematics 2018-12-26 Longfei Gao , David Keyes

We consider the Virtual Element discretization of the Navier-Stokes equations coupled with the heat equation where the viscosity depends on the temperature. We present the Virtual Element discretization of the coupled problem, show its…

Numerical Analysis · Mathematics 2022-05-03 Paola Francesca Antonietti , Giuseppe Vacca , Marco Verani

We study the motion of the steady compressible heat conducting viscous fluid in a bounded three dimensional domain governed by the compressible Navier-Stokes-Fourier system. Our main result is the existence of a weak solution to these…

Analysis of PDEs · Mathematics 2007-09-24 Piotr B. Mucha , Milan Pokorny

This paper studies a model of two-phase flow with an immersed material viscous interface and a finite element method for numerical solution of the resulting system of PDEs. The interaction between the bulk and surface media is characterized…

Numerical Analysis · Mathematics 2021-06-08 Maxim Olshanskii , Annalisa Quaini , Qi Sun

We investigate discretization strategies for a recently introduced class of energy-based models. The model class encompasses classical port-Hamiltonian systems, generalized gradient flows, and certain systems with algebraic constraints. Our…

Numerical Analysis · Mathematics 2026-05-29 Robert Altmann , Attila Karsai , Philipp Schulze

We describe a fully discrete mixed finite element method for the linearized rotating shallow water model, possibly with damping. While Crank-Nicolson time-stepping conserves energy in the absence of drag or forcing terms and is not subject…

Numerical Analysis · Mathematics 2020-03-04 Tate Kernell , Robert C. Kirby

We are interested in the discretisation of a drift-diffusion system in the framework of hybrid finite volume (HFV) methods on general polygonal/polyhedral meshes. The system under study is composed of two anisotropic and nonlinear…

Numerical Analysis · Mathematics 2023-05-11 Julien Moatti

This work develops a convergence theory for H(div)-conforming finite element methods applied to the steady Oseen problem, focusing on cases where the exact finite element complex holds while the commuting diagram property may fail. The…

Numerical Analysis · Mathematics 2025-12-01 Jin Zhang , Xiaowei Liu

In this paper we analyze a fully discrete scheme for a general Cahn-Hilliard equation coupled with a nonsteady Magneto-hydrodynamics flow, which describes two immiscible, incompressible and electrically conducting fluids with different…

Numerical Analysis · Mathematics 2022-02-04 Hailong Qiu

This paper addresses a nonstationary flow of heat-conductive incompressible Newtonian fluid with temperature-dependent viscosity coupled with linear heat transfer with advection and a viscous heat source term, under Navier/Dirichlet…

Analysis of PDEs · Mathematics 2011-11-15 Luisa Consiglieri