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In this paper, we introduce and analyse a surface finite element discretization of advection-diffusion equations with uncertain coefficients on evolving hypersurfaces. After stating unique solvability of the resulting semi-discrete problem,…

Numerical Analysis · Mathematics 2017-09-26 Ana Djurdjevac , Charles M. Elliott , Ralf Kornhuber , Thomas Ranner

We deal with the rigorous homogenization and dimension reduction of flow and transport problems posed in thin $\varepsilon$-periodic perforated layers with thickness of order $\varepsilon^{\alpha}$ with $\alpha \in (0,1)$ and therefore the…

Analysis of PDEs · Mathematics 2025-12-05 Markus Gahn , Vlad Revnic

Over three decades ago the advection-diffusion equation for a steady fluid velocity field was homogenized, leading to a Stieltjes integral representation for the effective diffusivity, which is given in terms of a spectral measure of a…

Fluid Dynamics · Physics 2024-04-30 N. B. Murphy , D. Hallman , E. Cherkaev , J. Xin , K. M. Golden

Diffusion-driven flow is a boundary layer flow arising from the interplay of gravity and diffusion in density-stratified fluids when a gravitational field is non-parallel to an impermeable solid boundary. This study investigates…

Fluid Dynamics · Physics 2024-09-23 Lingyun Ding

This paper presents a multi-scale method for convection-dominated diffusion problems in the regime of large P\'eclet numbers. The application of the solution operator to piecewise constant right-hand sides on some arbitrary coarse mesh…

Numerical Analysis · Mathematics 2022-06-07 Francesca Bonizzoni , Philip Freese , Daniel Peterseim

This paper concerns the use of asymptotic expansions for the efficient solving of forward and inverse problems involving a nonlinear singularly perturbed time-dependent reaction--diffusion--advection equation. By using an asymptotic…

Numerical Analysis · Mathematics 2023-02-15 Dmitrii Chaikovskii , Ye Zhang

In this research note we provide a variational basis for the optimal artificial diffusion method, which has been a cornerstone in developing many stabilized methods. The optimal artificial diffusion method produces exact nodal solutions…

Computational Engineering, Finance, and Science · Computer Science 2015-03-13 K. B. Nakshatrala , A. J. Valocchi

By combining concepts from particle-in-cell (PIC) and hybridized discontinuous Galerkin (HDG) methods, we present a particle-mesh scheme which allows for diffusion-free advection, satisfies mass and momentum conservation principles in a…

Numerical Analysis · Mathematics 2018-06-27 Jakob M. Maljaars , Robert Jan Labeur , Nathaniel Trask , Deborah Sulsky

This paper is concerned with a strongly degenerate convection-diffusion equation in one space dimension whose convective flux involves a non-linear function of the total mass to one side of the given position. This equation can be…

Numerical Analysis · Mathematics 2010-07-12 Fernando Betancourt , Raimund Bürger , Kenneth H. Karlsen

We describe how to solve the problem of Taylor dispersion in the presence of absorbing boundaries using an exact stochastic formulation. In addition to providing a clear stochastic picture of Taylor dispersion, our method leads to…

Statistical Mechanics · Physics 2013-11-25 Rudro R. Biswas , Pabitra N. Sen

We propose a new unfitted finite element method for simulation of two-phase flows in presence of insoluble surfactant. The key features of the method are 1) discrete conservation of surfactant mass; 2) the possibility of having meshes that…

Numerical Analysis · Mathematics 2022-11-30 Thomas Frachon , Sara Zahedi

We consider a singularly perturbed convection-diffusion problem that has in addition a shift term. We show a solution decomposition using asymptotic expansions and a stability result. Based upon this we provide a numerical analysis of high…

Numerical Analysis · Mathematics 2022-07-20 Mirjana Brdar , Sebastian Franz , Lars Ludwig , Hans-Görg Roos

Conventional mathematical models for simulating incompressible fluid flow problems are based on the Navier-Stokes equations expressed in terms of pressure and velocity. In this context, pressure-velocity coupling is a key issue, and…

Mathematical Physics · Physics 2025-06-06 Ricardo Costa , Stéphane Clain , Gaspar J. Machado , João M. Nóbrega

We introduce an automatic variationally stable analysis (AVS) for finite element (FE) computations of scalar-valued convection-diffusion equations with non-constant and highly oscillatory coefficients. In the spirit of least squares FE…

Numerical Analysis · Mathematics 2019-04-16 Victor M. Calo , Albert Romkes , Eirik Valseth

The solution of nonsymmetric but positive definite (NSPD) systems arising from advection-diffusion problems is an important research topic in science and engineering. Balancing domain decomposition by constraints with an adaptive coarse…

Numerical Analysis · Mathematics 2025-08-19 Jie Peng , Shi Shu , Junxian Wang , Liuqiang Zhong

We consider for a small parameter $\varepsilon >0$ a parabolic convection-diffusion problem with P\'eclet number of order $\mathcal{O}(\varepsilon^{-1})$ in a three-dimensional graph-like junction consisting of thin curvilinear cylinders…

Analysis of PDEs · Mathematics 2024-06-24 Taras Mel'nyk , Christian Rohde

Advection-diffusion problems of magnetic field and tracer field are analyzed using the field theoretic perturbative renormalization group. Both advected fields are considered to be passive, i.e., without any influence on the turbulent…

Chaotic Dynamics · Physics 2019-09-20 N. V. Antonov , N. M. Gulitskiy , M. M. Kostenko , T. Lučivjanský

This dissertation resolves a longstanding discussion of a mathematical problem important in contaminant hydrogeology and chemical-reaction engineering, the proper mathematical description for a miscible solute undergoing longitudinal…

Analysis of PDEs · Mathematics 2007-05-23 W. J. Golz

The main contribution of this paper is twofold: (1) Recently, Iyer, Xu, and Zlato\v{s} studied the dissipation enhancement by cellular flows based on standard advection-diffusion equations via a stochastic method. We generalize their…

Analysis of PDEs · Mathematics 2022-11-01 Yu Feng , Xiaoqian Xu

We address an original approach for the convergence analysis of a finite-volume scheme for the approximation of a stochastic diffusion-convection equation with multiplicative noise in a bounded domain of $\mathbb{R}^d$ (with $d=2$ or $3$)…

Numerical Analysis · Mathematics 2024-02-20 Caroline Bauzet , Kerstin Schmitz , Aleksandra Zimmermann