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Esaim-Mathematical Modelling and Numerical Analysis-Modelisation Mathematique et Analyse Numerique最新文献

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A non-local macroscopic model for traffic flow 交通流的非局部宏观模型
IF 1.9 3区 数学
Esaim-Mathematical Modelling and Numerical Analysis-Modelisation Mathematique et Analyse Numerique Pub Date : 2021-03-01 DOI: 10.1051/M2AN/2021006
Ioana Ciotir, Rima Fayad, N. Forcadel, A. Tonnoir
{"title":"A non-local macroscopic model for traffic flow","authors":"Ioana Ciotir, Rima Fayad, N. Forcadel, A. Tonnoir","doi":"10.1051/M2AN/2021006","DOIUrl":"https://doi.org/10.1051/M2AN/2021006","url":null,"abstract":"In this work, we propose a non-local Hamilton–Jacobi model for traffic flow and we prove the existence and uniqueness of the solution of this model. This model is justified as the limit of a rescaled microscopic model. We also propose a numerical scheme and we prove an estimate error between the continuous solution of this problem and the numerical one. Finally, we provide some numerical illustrations.","PeriodicalId":50499,"journal":{"name":"Esaim-Mathematical Modelling and Numerical Analysis-Modelisation Mathematique et Analyse Numerique","volume":"26 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2021-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87396363","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: 3
Various choices of source terms for a class of two-fluid two-velocity models 一类双流体双速度模型的源项的各种选择
IF 1.9 3区 数学
Esaim-Mathematical Modelling and Numerical Analysis-Modelisation Mathematique et Analyse Numerique Pub Date : 2021-03-01 DOI: 10.1051/M2AN/2020089
O. Hurisse
{"title":"Various choices of source terms for a class of two-fluid two-velocity models","authors":"O. Hurisse","doi":"10.1051/M2AN/2020089","DOIUrl":"https://doi.org/10.1051/M2AN/2020089","url":null,"abstract":"The source terms of the Baer–Nunziato model involve highly non-linear return to equilibrium terms. In order to perform numerical simulations of realistic situations, accounting for this relaxation effects is mandatory. Unfortunately, with the classical forms retained for these source terms in the literature, building efficient, robust and accurate numerical schemes is a tricky task. In this paper, we propose different non-classical forms for these source terms. As for the classical ones, they all agree with the second law of thermodynamics and they are thus associated with a growth of an entropy. The great advantage of some of these new forms of source terms is that they are more linear with respect to the conservative variables. Consequently, this allows to propose more robust, efficient and accurate numerical schemes, in particular when considering fractional step approaches for which source terms and convection terms are solved separately.","PeriodicalId":50499,"journal":{"name":"Esaim-Mathematical Modelling and Numerical Analysis-Modelisation Mathematique et Analyse Numerique","volume":"16 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2021-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85051629","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: 5
The Adaptive Biasing Force algorithm with non-conservative forces and related topics 非保守力的自适应偏置力算法及相关课题
IF 1.9 3区 数学
Esaim-Mathematical Modelling and Numerical Analysis-Modelisation Mathematique et Analyse Numerique Pub Date : 2021-02-19 DOI: 10.1051/m2an/2022010
T. Lelièvre, Lise Maurin, Pierre Monmarch'e
{"title":"The Adaptive Biasing Force algorithm with non-conservative forces and related topics","authors":"T. Lelièvre, Lise Maurin, Pierre Monmarch'e","doi":"10.1051/m2an/2022010","DOIUrl":"https://doi.org/10.1051/m2an/2022010","url":null,"abstract":"We propose a study of the Adaptive Biasing Force method's robustness under generic (possibly non-conservative) forces. We first ensure the flat histogram property is satisfied in all cases. We then introduce a fixed point problem yielding the existence of a stationary state for both the Adaptive Biasing Force and Projected Adapted Biasing Force algorithms, relying on generic bounds on the invariant probability measures of homogeneous diffusions. Using classical entropy techniques, we prove the exponential convergence of both biasing force and law as time goes to infinity, for both the Adaptive Biasing Force and the Projected Adaptive Biasing Force methods.","PeriodicalId":50499,"journal":{"name":"Esaim-Mathematical Modelling and Numerical Analysis-Modelisation Mathematique et Analyse Numerique","volume":"8 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2021-02-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90212723","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: 0
Positivity-preserving methods for ordinary differential equations 常微分方程的保正方法
IF 1.9 3区 数学
Esaim-Mathematical Modelling and Numerical Analysis-Modelisation Mathematique et Analyse Numerique Pub Date : 2021-02-16 DOI: 10.1051/m2an/2022042
S. Blanes, A. Iserles, S. MacNamara
{"title":"Positivity-preserving methods for ordinary differential equations","authors":"S. Blanes, A. Iserles, S. MacNamara","doi":"10.1051/m2an/2022042","DOIUrl":"https://doi.org/10.1051/m2an/2022042","url":null,"abstract":"Many important applications are modelled by differential equations with positive solutions. However, it remains an outstanding open problem to develop numerical methods that are both (i) of a high order of accuracy and (ii) capable of preserving positivity. It is known that the two main families of numerical methods, Runge-Kutta methods and multistep methods, face an order barrier. If they preserve positivity, then they are constrained to low accuracy: they cannot be better than first order. We propose novel methods that overcome this barrier: second order methods that preserve positivity unconditionally and a third order method that preserves positivity under very mild conditions. Our methods apply to a large class of differential equations that have a special graph Laplacian structure, which we elucidate. The equations need be neither linear nor autonomous and the graph Laplacian need not be symmetric. This algebraic structure arises naturally in many important applications where positivity is required. We showcase our new methods on applications where standard high order methods fail to preserve positivity, including infectious diseases, Markov processes, master equations and chemical reactions.","PeriodicalId":50499,"journal":{"name":"Esaim-Mathematical Modelling and Numerical Analysis-Modelisation Mathematique et Analyse Numerique","volume":"41 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2021-02-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88077856","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: 14
Mathematical modeling and numerical analysis for the higher order Boussinesq system 高阶Boussinesq系统的数学建模与数值分析
IF 1.9 3区 数学
Esaim-Mathematical Modelling and Numerical Analysis-Modelisation Mathematique et Analyse Numerique Pub Date : 2021-02-16 DOI: 10.1051/m2an/2022015
Bashar Bhorbatly, R. Lteif, Samer Israwi, S. Gerbi
{"title":"Mathematical modeling and numerical analysis for the higher order Boussinesq system","authors":"Bashar Bhorbatly, R. Lteif, Samer Israwi, S. Gerbi","doi":"10.1051/m2an/2022015","DOIUrl":"https://doi.org/10.1051/m2an/2022015","url":null,"abstract":"This study deals with higher-ordered asymptotic equations for the water-waves problem. We considered the higher-order/extended Boussinesq equations over a flat bottom topography in the well-known long wave regime. Providing an existence and uniqueness of solution on a relevant time scale of order 1/ [[EQUATION]]   and showing that the solution's behavior is close to the solution of the  water waves equations with a better precision corresponding to initial data, the asymptotic model is well-posed in the sense of Hadamard. Then we compared several water waves solitary solutions with respect to the numerical solution of our model. At last, we solve explicitly this model and validate the results numerically.","PeriodicalId":50499,"journal":{"name":"Esaim-Mathematical Modelling and Numerical Analysis-Modelisation Mathematique et Analyse Numerique","volume":"13 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2021-02-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83772354","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: 5
A homogeneous relaxation low mach number model 齐次松弛低马赫数模型
IF 1.9 3区 数学
Esaim-Mathematical Modelling and Numerical Analysis-Modelisation Mathematique et Analyse Numerique Pub Date : 2021-02-13 DOI: 10.1051/M2AN/2021032
Gloria Faccanoni, Bérénice Grec, Y. Penel
{"title":"A homogeneous relaxation low mach number model","authors":"Gloria Faccanoni, Bérénice Grec, Y. Penel","doi":"10.1051/M2AN/2021032","DOIUrl":"https://doi.org/10.1051/M2AN/2021032","url":null,"abstract":"In the present paper, we investigate a new homogeneous relaxation model describing the behaviour of a two-phase fluid flow in a low Mach number regime, which can be obtained as a low Mach number approximation of the well-known HRM. For this specific model, we derive an equation of state to describe the thermodynamics of the two-phase fluid. We prove some theoretical properties satisfied by the solutions of the model, and provide a well-balanced scheme. To go further, we investigate the instantaneous relaxation regime, and prove the formal convergence of this model towards the low Mach number approximation of the well-known HEM. An asymptotic-preserving scheme is introduced to allow numerical simulations of the coupling between spatial regions with different relaxation characteristic times.","PeriodicalId":50499,"journal":{"name":"Esaim-Mathematical Modelling and Numerical Analysis-Modelisation Mathematique et Analyse Numerique","volume":"81 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2021-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88296184","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
Asymptotic analysis for periodic perforated shells 周期穿孔壳的渐近分析
IF 1.9 3区 数学
Esaim-Mathematical Modelling and Numerical Analysis-Modelisation Mathematique et Analyse Numerique Pub Date : 2021-01-01 DOI: 10.1051/M2AN/2020067
G. Griso, Michael Hauck, J. Orlik
{"title":"Asymptotic analysis for periodic perforated shells","authors":"G. Griso, Michael Hauck, J. Orlik","doi":"10.1051/M2AN/2020067","DOIUrl":"https://doi.org/10.1051/M2AN/2020067","url":null,"abstract":"We consider a perforated half-cylindrical thin shell and investigate the limit behavior when the period and the thickness simultaneously go to zero. By using the decomposition of shell displacements presented in Griso [JMPA 89 (2008) 199–223] we obtain a priori estimates. With the unfolding and rescaling operator we transform the problem to a reference configuration. In the end this yields a homogenized limit problem for the shell.","PeriodicalId":50499,"journal":{"name":"Esaim-Mathematical Modelling and Numerical Analysis-Modelisation Mathematique et Analyse Numerique","volume":"4 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87867255","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
Central discontinuous Galerkin methods on overlapping meshes for wave equations 波浪方程重叠网格的中心不连续Galerkin方法
IF 1.9 3区 数学
Esaim-Mathematical Modelling and Numerical Analysis-Modelisation Mathematique et Analyse Numerique Pub Date : 2021-01-01 DOI: 10.1051/m2an/2020069
Yong Liu, Jianfang Lu, Chi-Wang Shu, Mengping Zhang
{"title":"Central discontinuous Galerkin methods on overlapping meshes for wave equations","authors":"Yong Liu, Jianfang Lu, Chi-Wang Shu, Mengping Zhang","doi":"10.1051/m2an/2020069","DOIUrl":"https://doi.org/10.1051/m2an/2020069","url":null,"abstract":"In this paper, we study the central discontinuous Galerkin (DG) method on overlapping meshes for second order wave equations. We consider the first order hyperbolic system, which is equivalent to the second order scalar equation, and construct the corresponding central DG scheme. We then provide the stability analysis and the optimal error estimates for the proposed central DG scheme for one- and multi-dimensional cases with piecewise Pk elements. The optimal error estimates are valid for uniform Cartesian meshes and polynomials of arbitrary degree k ≥ 0. In particular, we adopt the techniques in Liu et al. (SIAM J. Numer. Anal. 56 (2018) 520–541; ESAIM: M2AN 54 (2020) 705–726) and obtain the local projection that is crucial in deriving the optimal order of convergence. The construction of the projection here is more challenging since the unknowns are highly coupled in the proposed scheme. Dispersion analysis is performed on the proposed scheme for one dimensional problems, indicating that the numerical solution with P1 elements reaches its minimum with a suitable parameter in the dissipation term. Several numerical examples including accuracy tests and long time simulation are presented to validate the theoretical results.","PeriodicalId":50499,"journal":{"name":"Esaim-Mathematical Modelling and Numerical Analysis-Modelisation Mathematique et Analyse Numerique","volume":"16 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76628903","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
Non-local variant of the optimised Schwarz method for arbitrary non-overlapping subdomain partitions 任意非重叠子域划分的优化Schwarz方法的非局部变体
IF 1.9 3区 数学
Esaim-Mathematical Modelling and Numerical Analysis-Modelisation Mathematique et Analyse Numerique Pub Date : 2020-12-04 DOI: 10.1051/m2an/2020083
X. Claeys
{"title":"Non-local variant of the optimised Schwarz method for arbitrary non-overlapping subdomain partitions","authors":"X. Claeys","doi":"10.1051/m2an/2020083","DOIUrl":"https://doi.org/10.1051/m2an/2020083","url":null,"abstract":"We consider a scalar wave propagation in harmonic regime modelled by Helmholtz equation with heterogeneous coefficients. Using the Multi-Trace Formalism (MTF), we propose a new variant of the Optimized Schwarz Method (OSM) that remains valid in the presence of cross-points in the subdomain partition. This leads to the derivation of a strongly coercive formulation of our Helmholtz problem posed on the union of all interfaces. The corresponding operator takes the form “identity + non-expansive”.","PeriodicalId":50499,"journal":{"name":"Esaim-Mathematical Modelling and Numerical Analysis-Modelisation Mathematique et Analyse Numerique","volume":"28 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2020-12-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82540645","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: 13
Analysis of a hybridizable discontinuous Galerkin scheme for the tangential control of the Stokes system Stokes系统切向控制的可混合间断Galerkin格式分析
IF 1.9 3区 数学
Esaim-Mathematical Modelling and Numerical Analysis-Modelisation Mathematique et Analyse Numerique Pub Date : 2020-11-01 DOI: 10.1051/m2an/2020015
W. Gong, Weiwei Hu, M. Mateos, J. Singler, Yangwen Zhang
{"title":"Analysis of a hybridizable discontinuous Galerkin scheme for the tangential control of the Stokes system","authors":"W. Gong, Weiwei Hu, M. Mateos, J. Singler, Yangwen Zhang","doi":"10.1051/m2an/2020015","DOIUrl":"https://doi.org/10.1051/m2an/2020015","url":null,"abstract":"We consider an unconstrained tangential Dirichlet boundary control problem for the Stokes equations with an L 2 penalty on the boundary control. The contribution of this paper is twofold. First, we obtain well-posedness and regularity results for the tangential Dirichlet control problem on a convex polygonal domain. The analysis contains new features not found in similar Dirichlet control problems for the Poisson equation; an interesting result is that the optimal control has higher local regularity on the individual edges of the domain compared to the global regularity on the entire boundary. Second, we propose and analyze a hybridizable discontinuous Galerkin (HDG) method to approximate the solution. For convex polygonal domains, our theoretical convergence rate for the control is optimal with respect to the global regularity on the entire boundary. We present numerical experiments to demonstrate the performance of the HDG method.","PeriodicalId":50499,"journal":{"name":"Esaim-Mathematical Modelling and Numerical Analysis-Modelisation Mathematique et Analyse Numerique","volume":"54 1","pages":"2229-2264"},"PeriodicalIF":1.9,"publicationDate":"2020-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45159999","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
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