Esaim-Mathematical Modelling and Numerical Analysis-Modelisation Mathematique et Analyse Numerique最新文献_第9页

A hybridizable discontinuous Galerkin method for second order elliptic equations with Dirac delta source 二阶椭圆方程的可杂化不连续Galerkin方法

IF 1.9 3区数学

Esaim-Mathematical Modelling and Numerical Analysis-Modelisation Mathematique et Analyse Numerique Pub Date : 2022-01-14 DOI: 10.1051/m2an/2022005

Haitao Leng, Yanping Chen

引用次数: 4

Convergence analysis of two finite element methods for the modified Maxwell's Steklov eigenvalue problem 修正Maxwell's Steklov特征值问题两种有限元方法的收敛性分析

IF 1.9 3区数学

Esaim-Mathematical Modelling and Numerical Analysis-Modelisation Mathematique et Analyse Numerique Pub Date : 2022-01-10 DOI: 10.1051/m2an/2022001

Bo Gong

引用次数: 3

Fully-discrete, decoupled, second-order time-accurate and energy stable finite element numerical scheme of the Cahn-Hilliard binary surfactant model confined in the Hele-Shaw cell Hele-Shaw槽内Cahn-Hilliard二元表面活性剂模型的全离散、解耦、二阶时准和能量稳定有限元格式

IF 1.9 3区数学

Esaim-Mathematical Modelling and Numerical Analysis-Modelisation Mathematique et Analyse Numerique Pub Date : 2022-01-06 DOI: 10.1051/m2an/2022003

Xiaofeng Yang

{"title":"Fully-discrete, decoupled, second-order time-accurate and energy stable finite element numerical scheme \u0000\u0000of the Cahn-Hilliard binary surfactant model confined in the Hele-Shaw cell","authors":"Xiaofeng Yang","doi":"10.1051/m2an/2022003","DOIUrl":"https://doi.org/10.1051/m2an/2022003","url":null,"abstract":"We consider the numerical approximation of the binary fluid surfactant phase-field model confined in a Hele-Shaw cell, where the system includes two coupled Cahn-Hilliard equations and Darcy equations. We develop a fully-discrete finite element scheme with some desired characteristics, including linearity, second-order time accuracy, decoupling structure, and unconditional energy stability. The scheme is constructed by combining the projection method for the Darcy equation, the quadratization approach for the nonlinear energy potential, and a decoupling method of using a trivial ODE built upon the ``{zero-energy-contribution}\" feature. The advantage of this scheme is that not only can all variables be calculated in a decoupled manner, but each equation has only constant coefficients at each time step. We strictly prove that the scheme satisfies the unconditional energy stability and give a detailed implementation process. Various numerical examples are further carried out to prove the effectiveness of the scheme, in which the benchmark Saffman-Taylor fingering instability problems in various flow regimes are simulated to verify the weakening effects of surfactant on surface tension.","PeriodicalId":50499,"journal":{"name":"Esaim-Mathematical Modelling and Numerical Analysis-Modelisation Mathematique et Analyse Numerique","volume":"93 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2022-01-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90491267","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 4

Infection spreading in cell culture as a reaction-diffusion wave 感染以反应扩散波的形式在细胞培养中传播

IF 1.9 3区数学

Esaim-Mathematical Modelling and Numerical Analysis-Modelisation Mathematique et Analyse Numerique Pub Date : 2022-01-01 DOI: 10.1051/m2an/2022019

Mahiout Bessonov Nikolai Kazmierczak Bogdan Sadaka Georges Latifa Ait

{"title":"Infection spreading in cell culture as a reaction-diffusion wave","authors":"Mahiout Bessonov Nikolai Kazmierczak Bogdan Sadaka Georges Latifa Ait","doi":"10.1051/m2an/2022019","DOIUrl":"https://doi.org/10.1051/m2an/2022019","url":null,"abstract":"Infection spreading in cell culture occurs due to virus replication in infected cells and its random motion in the extracellular space. Multiplicity of infection experiments in cell cultures are conventionally used for the characterization of viral infection by the number of viral plaques and the rate of their growth. We describe this process with a delay reaction-diffusion system of equations for the concentrations of uninfected cells, infected cells, virus, and interferon. Time delay corresponds to the duration of viral replication inside infected cells. We show that infection propagates in cell culture as a reaction-diffusion wave, we determine the wave speed and prove its existence. Next, we carry out numerical simulations and identify three stages of infection progression: infection decay during time delay due to virus replication, explosive growth of viral load when infected cells begin to reproduce it, and finally, wave-like infection progression in cell culture characterized by a constant or slowly growing total viral load. The modelling results are in agreement with the experimental data for the coronavirus infection in a culture of epithelial cells and for some other experiments. The presence of interferon produced by infected cells decreases the viral load but does not change the speed of infection progression in cell culture. In the 2D modelling, the total viral load grows faster than in the 1D case due to the increase of plaque perimeter. © 2022 The authors. Published by EDP Sciences, SMAI.","PeriodicalId":50499,"journal":{"name":"Esaim-Mathematical Modelling and Numerical Analysis-Modelisation Mathematique et Analyse Numerique","volume":"44 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79955294","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 10

Asymptotic derivation of multicomponent compressible flows with heat conduction and mass diffusion 具有热传导和质量扩散的多分量可压缩流的渐近推导

IF 1.9 3区数学

Esaim-Mathematical Modelling and Numerical Analysis-Modelisation Mathematique et Analyse Numerique Pub Date : 2021-12-27 DOI: 10.1051/m2an/2022065

S. Georgiadis, A. Tzavaras

引用次数: 3

Analysis of a diffuse interface method for the Stokes-Darcy coupled problem Stokes-Darcy耦合问题的扩散界面法分析

IF 1.9 3区数学

Esaim-Mathematical Modelling and Numerical Analysis-Modelisation Mathematique et Analyse Numerique Pub Date : 2021-12-23 DOI: 10.1051/m2an/2023062

Martina Bukavc, B. Muha, A. Salgado

引用次数: 0

Convergence of nonlinear numerical approximations foran elliptic linear problem with irregular data 具有不规则数据的椭圆型线性问题非线性数值逼近的收敛性

IF 1.9 3区数学

Esaim-Mathematical Modelling and Numerical Analysis-Modelisation Mathematique et Analyse Numerique Pub Date : 2021-11-29 DOI: 10.1051/m2an/2021079

R. Eymard, David Maltese

{"title":"Convergence of nonlinear numerical approximations for\u0000\u0000an elliptic linear problem with irregular data","authors":"R. Eymard, David Maltese","doi":"10.1051/m2an/2021079","DOIUrl":"https://doi.org/10.1051/m2an/2021079","url":null,"abstract":"This work is devoted to the study of the approximation, using two nonlinear numerical methods, of a linear elliptic problem with measure data and heterogeneous anisotropic diffusion matrix. Both methods show convergence properties to a continuous solution of the problem in a weak sense, through the change of variable u = ψ(v), where ψ is a well chosen diffeomorphism between (−1, 1) and R, and v is valued in (−1, 1). We first study a nonlinear finite element approximation on any simplicial grid. We prove the\u0000\u0000existence of a discrete solution, and, under standard regularity conditions, we prove its convergence to a weak solution of the problem by applying Hölder and Sobolev inequalities. Some numerical results, in 2D and 3D cases where the solution does not belong to H 1(Ω), show that this method can provide accurate results. We then construct a numerical scheme which presents a convergence property to the entropy weak solution of the problem in the case where the right-hand side belongs to L1 . This is achieved owing to a nonlinear control volume finite element (CVFE) method, keeping the same nonlinear reformulation, and adding an upstream weighting evaluation and a nonlinear p−Laplace vanishing stabilisation term.","PeriodicalId":50499,"journal":{"name":"Esaim-Mathematical Modelling and Numerical Analysis-Modelisation Mathematique et Analyse Numerique","volume":"101 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2021-11-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80628061","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 1

Diffusive limits of 2D well-balanced schemesfor kinetic models of neutron transport 中子输运动力学模型二维平衡格式的扩散极限

IF 1.9 3区数学

Esaim-Mathematical Modelling and Numerical Analysis-Modelisation Mathematique et Analyse Numerique Pub Date : 2021-11-18 DOI: 10.1051/m2an/2021077

G. Bretti, L. Gosse, N. Vauchelet

引用次数: 2

Local defect-correction method based on multilevel discretization for Steklov eigenvalue problem 基于多级离散化的Steklov特征值问题局部缺陷校正方法

IF 1.9 3区数学

Esaim-Mathematical Modelling and Numerical Analysis-Modelisation Mathematique et Analyse Numerique Pub Date : 2021-11-17 DOI: 10.1051/m2an/2021076

Fei Xu, Liu Chen, Qiumei Huang

{"title":"Local defect-correction method based on multilevel discretization for Steklov eigenvalue problem","authors":"Fei Xu, Liu Chen, Qiumei Huang","doi":"10.1051/m2an/2021076","DOIUrl":"https://doi.org/10.1051/m2an/2021076","url":null,"abstract":"In this paper, we propose a local defect-correction method for solving the Steklov eigenvalue problem arising from the scalar second order positive definite partial differential equations based on the multilevel discretization. The objective is to avoid solving large-scale equations especially the large-scale Steklov eigenvalue problem whose computational cost increases exponentially. The proposed algorithm transforms the Steklov eigenvalue problem into a series of linear boundary value problems, which are defined in a multigrid space sequence, and a series of small-scale Steklov eigenvalue problems in a coarse correction space. Furthermore, we use the local defect-correction technique to divide the large-scale boundary value problems into small-scale subproblems. Through our proposed algorithm, we avoid solving large-scale Steklov eigenvalue problems. As a result, our proposed algorithm demonstrates significantly improved the solving efficiency. Additionally, we conduct numerical experiments and a rigorous theoretical analysis to verify the effectiveness of our proposed approach.","PeriodicalId":50499,"journal":{"name":"Esaim-Mathematical Modelling and Numerical Analysis-Modelisation Mathematique et Analyse Numerique","volume":"93 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2021-11-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81240991","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 2

An analysis of the unified formulation for the equilibrium problem of compositional multiphase mixtures 组份多相混合物平衡问题的统一公式分析

IF 1.9 3区数学

Esaim-Mathematical Modelling and Numerical Analysis-Modelisation Mathematique et Analyse Numerique Pub Date : 2021-11-16 DOI: 10.1051/m2an/2021075

Ibtihel Ben Gharbia, M. Haddou, Quang Huy Tran, Duc Thach Son Vu

{"title":"An analysis of the unified formulation for the equilibrium problem of compositional multiphase mixtures","authors":"Ibtihel Ben Gharbia, M. Haddou, Quang Huy Tran, Duc Thach Son Vu","doi":"10.1051/m2an/2021075","DOIUrl":"https://doi.org/10.1051/m2an/2021075","url":null,"abstract":"In this paper , we conduct a thorough mathematical analysis of the unified formulation advocated by Lauser et al . [ Adv . Water Res . 34 (2011), 957-966] for compositional multiphase flows in porous media . The interest of this formulation lies in its potential to automatically handle the appearance and disappearance of phases. However , its practical implementation turned out to be not always robust for realistic fugacity laws associated with cubic equations of state , as shown by Ben Gharbia and Flauraud [ Oil & Gas Sci . Technol . 74 (2019), 43]. By focusing on the subproblem of phase equilibrium , we derive sufficient conditions for the existence of the corresponding system of equations. We trace back the difficulty of cubic laws to a deficiency of the Gibbs functions that comes into play due to the `` unifying '' feature of the new formulation. We propose a partial remedy for this problem by extending the domain of definition of these functions in a natural way . Besides , we highlight the crucial but seemingly unknown fact that the unified formulation encapsulates all the properties known to physicists on phase equilibrium , such as the tangent plane criterion and the minimization of the Gibbs energy of the mixture.","PeriodicalId":50499,"journal":{"name":"Esaim-Mathematical Modelling and Numerical Analysis-Modelisation Mathematique et Analyse Numerique","volume":"35 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2021-11-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84324686","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 1