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A hybrid-dG method for singularly perturbed convection-diffusion equations on pipe networks 管网上奇摄动对流扩散方程的混合dg方法
IF 1.9 3区 数学
Esaim-Mathematical Modelling and Numerical Analysis-Modelisation Mathematique et Analyse Numerique Pub Date : 2023-05-18 DOI: 10.1051/m2an/2023044
N. Philippi, H. Egger
{"title":"A hybrid-dG method for singularly perturbed convection-diffusion equations on pipe networks","authors":"N. Philippi, H. Egger","doi":"10.1051/m2an/2023044","DOIUrl":"https://doi.org/10.1051/m2an/2023044","url":null,"abstract":"We study the numerical approximation of singularly perturbed convection-diffusion problems on one-dimensional pipe networks. In the vanishing diffusion limit, the number and type of boundary conditions and coupling conditions at network junctions change, which gives rise to singular layers at the outflow boundaries of the pipes. A hybrid discontinuous Galerkin method is proposed, which provides a natural upwind mechanism for the convection-dominated case.\u0000Moreover, the method provides a viable approximation for the limiting pure transport problem.\u0000A detailed analysis of the singularities of the solution and the discretization error is presented, and an adaptive strategy is proposed, leading to order optimal error estimates that hold uniformly in the singular perturbation limit. The theoretical results are confirmed by numerical tests.","PeriodicalId":50499,"journal":{"name":"Esaim-Mathematical Modelling and Numerical Analysis-Modelisation Mathematique et Analyse Numerique","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2023-05-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78391815","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
A conservative network element method for diffusion-advection-reaction problems 扩散-平流-反应问题的保守网络元法
IF 1.9 3区 数学
Esaim-Mathematical Modelling and Numerical Analysis-Modelisation Mathematique et Analyse Numerique Pub Date : 2023-05-05 DOI: 10.1051/m2an/2023040
J. Coatléven
{"title":"A conservative network element method for diffusion-advection-reaction problems","authors":"J. Coatléven","doi":"10.1051/m2an/2023040","DOIUrl":"https://doi.org/10.1051/m2an/2023040","url":null,"abstract":"We derive a conservative network element method for heterogeneous and anisotropic diffusion problems by modifying the non-conservative version, and extend it to the approximation of an additional advection term. The numerical scheme possesses the flux formulation reminiscent of classical finite volume methods. Its convergence is naturally governed by the network element theory. Numerical results illustrate the good behavior of the method even on distorted point clouds.","PeriodicalId":50499,"journal":{"name":"Esaim-Mathematical Modelling and Numerical Analysis-Modelisation Mathematique et Analyse Numerique","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2023-05-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82873433","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
A posteriori error estimates for the large eddy simulation applied to incompressible fluids 不可压缩流体大涡模拟的后验误差估计
IF 1.9 3区 数学
Esaim-Mathematical Modelling and Numerical Analysis-Modelisation Mathematique et Analyse Numerique Pub Date : 2023-05-04 DOI: 10.1051/m2an/2023039
Ghina Nassreddine, P. Omnes, Toni Sayah
{"title":"A posteriori error estimates for the large eddy simulation applied to incompressible fluids","authors":"Ghina Nassreddine, P. Omnes, Toni Sayah","doi":"10.1051/m2an/2023039","DOIUrl":"https://doi.org/10.1051/m2an/2023039","url":null,"abstract":"Abstract. We study the two dimensional time dependent Large Eddy Simulation method applied to the incompressible Navier-Stokes system with Smagorinsky’s eddy viscosity model and a filter width that depends on the local mesh size. The discrete model is based on the implicit Euler scheme and a conforming finite element method for the time and space discretizations, respectively. We establish a reliable and efficient a posteriori error estimation between the numerical LES solution and the exact solution of the original Navier-Stokes system, which involves three types of error indicators respectively related to the filter and to the discretizations in time and space. Numerical results show the effectiveness of adaptive simulations.","PeriodicalId":50499,"journal":{"name":"Esaim-Mathematical Modelling and Numerical Analysis-Modelisation Mathematique et Analyse Numerique","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2023-05-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73584124","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
A Nitsche method for the elastoplastic torsion problem 弹塑性扭转问题的Nitsche方法
IF 1.9 3区 数学
Esaim-Mathematical Modelling and Numerical Analysis-Modelisation Mathematique et Analyse Numerique Pub Date : 2023-04-24 DOI: 10.1051/m2an/2023034
F. Chouly, T. Gustafsson, P. Hild
{"title":"A Nitsche method for the elastoplastic torsion problem","authors":"F. Chouly, T. Gustafsson, P. Hild","doi":"10.1051/m2an/2023034","DOIUrl":"https://doi.org/10.1051/m2an/2023034","url":null,"abstract":"This study is concerned with the elastoplastic torsion problem, in dimension $ngeq1$, and in a polytopal, convex or not, domain. In the physically relevant case where the source term is a constant, this problem can be reformulated using the distance function to the boundary. We combine the aforementioned reformulation  with a Nitsche-type discretization as in [Burman, Erik, et al. Computer Methods in Applied Mechanics and Engineering 313 (2017): 362-374]. This has two advantages: 1) it leads to optimal error bounds in the natural norm, even for nonconvex domains; 2) it is easy to implement within most of finite element libraries. We establish the well-posedness and convergence properties of the method, and illustrate its behavior with numerical experiments.","PeriodicalId":50499,"journal":{"name":"Esaim-Mathematical Modelling and Numerical Analysis-Modelisation Mathematique et Analyse Numerique","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2023-04-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73760769","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
Reduced order modeling for elliptic problems with high contrast diffusion coefficients 高对比度扩散系数椭圆型问题的降阶建模
IF 1.9 3区 数学
Esaim-Mathematical Modelling and Numerical Analysis-Modelisation Mathematique et Analyse Numerique Pub Date : 2023-04-21 DOI: 10.1051/m2an/2023013
A. Cohen, Matthieu Dolbeault, A. Somacal, W. Dahmen
{"title":"Reduced order modeling for elliptic problems with high contrast diffusion coefficients","authors":"A. Cohen, Matthieu Dolbeault, A. Somacal, W. Dahmen","doi":"10.1051/m2an/2023013","DOIUrl":"https://doi.org/10.1051/m2an/2023013","url":null,"abstract":"We consider a parametric elliptic PDE with a scalar piecewise constant diffusion coefficient taking arbitrary positive values on fixed subdomains. This problem is not uniformly elliptic, as the contrast can be arbitrarily high, contrarily to the Uniform Ellipticity Assumption (UEA) that is com- monly made on parametric elliptic PDEs. We construct reduced model spaces that approximate uniformly well all solutions with estimates in relative error that are independent of the contrast level. These estimates are sub-exponential in the reduced model dimension, yet exhibiting the curse of dimensionality as the number of subdomains grows. Similar es- timates are obtained for the Galerkin projection, as well as for the state estimation and parameter estimation inverse problems. A key ingredient in our construction and analysis is the study of the convergence towards limit solutions of stiff problems when diffusion tends to infinity in certain domains.","PeriodicalId":50499,"journal":{"name":"Esaim-Mathematical Modelling and Numerical Analysis-Modelisation Mathematique et Analyse Numerique","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2023-04-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72393214","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
Study of an entropy dissipating finite volume scheme for a nonlocal cross-diffusion system                      非局部交叉扩散系统的熵耗散有限体积格式研究
IF 1.9 3区 数学
Esaim-Mathematical Modelling and Numerical Analysis-Modelisation Mathematique et Analyse Numerique Pub Date : 2023-04-04 DOI: 10.1051/m2an/2023032
A. Zurek, M. Herda
{"title":"Study of an entropy dissipating finite volume scheme for a nonlocal cross-diffusion system\u0000 \u0000 \u0000 \u0000 \u0000 \u0000 \u0000 \u0000 \u0000 \u0000 \u0000 \u0000 \u0000 \u0000 \u0000 \u0000 \u0000 \u0000 \u0000 \u0000 \u0000 ","authors":"A. Zurek, M. Herda","doi":"10.1051/m2an/2023032","DOIUrl":"https://doi.org/10.1051/m2an/2023032","url":null,"abstract":"Abstract. In this paper we analyse a finite volume scheme for a nonlocal version of the Shigesada-Kawazaki-Teramoto (SKT) cross-diffusion system. We prove the existence of solutions to the scheme, derive qualitative properties of the solutions and prove its convergence. The proofs rely on a discrete entropy-dissipation inequality, discrete compactness arguments, and on the novel adaptation of the so-called duality method at the discrete level. Finally, thanks to numerical experiments, we investigate the influence of the nonlocality in the system: on convergence properties of the scheme, as an approximation of the local system and on the development of diffusive instabilities.","PeriodicalId":50499,"journal":{"name":"Esaim-Mathematical Modelling and Numerical Analysis-Modelisation Mathematique et Analyse Numerique","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2023-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77218070","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
Finite element approximation of dielectrophoretic force driven flow problems 介电泳力驱动流动问题的有限元逼近
IF 1.9 3区 数学
Esaim-Mathematical Modelling and Numerical Analysis-Modelisation Mathematique et Analyse Numerique Pub Date : 2023-04-03 DOI: 10.1051/m2an/2023031
P. Gerstner, V. Heuveline
{"title":"Finite element approximation of dielectrophoretic force driven flow problems","authors":"P. Gerstner, V. Heuveline","doi":"10.1051/m2an/2023031","DOIUrl":"https://doi.org/10.1051/m2an/2023031","url":null,"abstract":"In this paper, we propose a full discretization scheme for the instationary thermal-electro-\u0000\u0000hydrodynamic (TEHD) Boussinesq equations. These equations model the dynamics of a non-isothermal,\u0000\u0000dielectric fluid under the influence of a dielectrophoretic (DEP) force. Our scheme combines an H 1 -\u0000\u0000conformal finite element method for spatial discretization with a backward differentiation formula\u0000\u0000(BDF) for time stepping. The resulting scheme allows for a decoupled solution of the individual parts\u0000\u0000of this multi-physics system. Moreover, we derive a priori convergence rates that are of first and sec-\u0000\u0000ond order in time, depending on how the individual ingredients of the BDF scheme are chosen and of\u0000\u0000optimal order in space. In doing so, special care is taken of modeling the DEP force, since its original\u0000\u0000form is a cubic term. The obtained error estimates are verified by numerical experiments.","PeriodicalId":50499,"journal":{"name":"Esaim-Mathematical Modelling and Numerical Analysis-Modelisation Mathematique et Analyse Numerique","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2023-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86145124","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
Efficient inequality-preserving integrators for differential equations satisfying forward Euler conditions 满足正演欧拉条件的微分方程的有效保不等式积分器
IF 1.9 3区 数学
Esaim-Mathematical Modelling and Numerical Analysis-Modelisation Mathematique et Analyse Numerique Pub Date : 2023-03-30 DOI: 10.1051/m2an/2023029
Hong Zhang, Xu Qian, Jun Xia, Songhe Song
{"title":"Efficient inequality-preserving integrators for differential equations satisfying forward Euler conditions","authors":"Hong Zhang, Xu Qian, Jun Xia, Songhe Song","doi":"10.1051/m2an/2023029","DOIUrl":"https://doi.org/10.1051/m2an/2023029","url":null,"abstract":"Developing explicit, high-order accurate, and stable algorithms for nonlinear differential equations remains an exceedingly difficult task. In this work, a systematic approach is proposed to develop high-order, large time-stepping schemes that can preserve inequality structures shared by a class of differential equations satisfying forward Euler conditions. Strong-stability-preserving (SSP) methods are popular and effective for solving equations of this type. However, few methods can deal with the situation when the time-step size is larger than that allowed by SSP methods. By adopting time-step-dependent stabilization and taking advantage of integrating factor methods in the Shu-Osher form, we propose enforcing the inequality structure preservation by approximating the exponential function using a novel recurrent approximation without harming the convergence. We define sufficient conditions for the obtained parametric Runge-Kutta (pRK) schemes to preserve inequality structures for any time-step size, namely, the underlying Shu-Osher coefficients are non-negative. To remove the requirement of a large stabilization term caused by stiff linear operators, we further develop inequality-preserving parametric integrating factor Runge-Kutta (pIFRK) schemes by incorporating the pRK with an integrating factor related to the stiff term, and enforcing the non-decreasing of abscissas. The only free parameter can be determined a priori based on the SSP coefficient, the time-step size, and the forward Euler condition. We demonstrate that the parametric methods developed here offer an effective and unified approach to study problems that satisfy forward Euler conditions, and cover a wide range of well-known models. Finally, numerical experiments reflect the high-order accuracy, efficiency, and inequality-preserving properties of the proposed schemes.","PeriodicalId":50499,"journal":{"name":"Esaim-Mathematical Modelling and Numerical Analysis-Modelisation Mathematique et Analyse Numerique","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2023-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80497167","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
A homogenized model accounting for dispersion, interfaces and source points for transient waves in 1D periodic media 一维周期介质中瞬态波的色散、界面和源点均质化模型
IF 1.9 3区 数学
Esaim-Mathematical Modelling and Numerical Analysis-Modelisation Mathematique et Analyse Numerique Pub Date : 2023-03-27 DOI: 10.1051/m2an/2023027
Rémi Cornaggia, B. Lombard
{"title":"A homogenized model accounting for dispersion, interfaces and source points for transient waves in 1D periodic media","authors":"Rémi Cornaggia, B. Lombard","doi":"10.1051/m2an/2023027","DOIUrl":"https://doi.org/10.1051/m2an/2023027","url":null,"abstract":"A homogenized model is proposed for linear waves in 1D microstructured media. It combines second-order asymptotic homogenization (to account for dispersion) and interface correctors (for transmission from or towards homogeneous media). A new bound on a second-order effective coefficient is proven, ensuring well-posedness of the homogenized model whatever the microstructure. Based on an analogy with existing enriched continua, the evolution equations are reformulated as a dispersive hyperbolic system. The efficiency of the model is illustrated via time-domain numerical simulations. An extension to Dirac source terms is also proposed.","PeriodicalId":50499,"journal":{"name":"Esaim-Mathematical Modelling and Numerical Analysis-Modelisation Mathematique et Analyse Numerique","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2023-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82962071","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
A staggered projection scheme for viscoelastic flows                                粘弹性流的交错投影格式
IF 1.9 3区 数学
Esaim-Mathematical Modelling and Numerical Analysis-Modelisation Mathematique et Analyse Numerique Pub Date : 2023-03-27 DOI: 10.1051/m2an/2023020
J. Latché, O. Mokhtari, Yohan Davit, M. Quintard
{"title":"A staggered projection scheme for viscoelastic flows\u0000 \u0000 \u0000 \u0000 \u0000 \u0000 \u0000 \u0000 \u0000 \u0000 \u0000 \u0000 \u0000 \u0000 \u0000 \u0000 \u0000 \u0000 \u0000 \u0000 \u0000 \u0000 \u0000 \u0000 \u0000 \u0000 \u0000 \u0000 \u0000 \u0000 \u0000 ","authors":"J. Latché, O. Mokhtari, Yohan Davit, M. Quintard","doi":"10.1051/m2an/2023020","DOIUrl":"https://doi.org/10.1051/m2an/2023020","url":null,"abstract":"We develop a numerical scheme for the flow of viscoelastic fluids, including the OldroydB and FENE-CR constitutive models. The space discretization is staggered, using either the Marker-And-Cell (MAC) scheme for structured nonuniform grids, or the Rannacher and Turek (RT) nonconforming low-order finite element approximation for general quandrangular or hexahedral meshes. The time discretization uses a fractional-step algorithm where the solution of the Navier-Stokes equations is first obtained by a projection method and then the transport-reaction equation for the conformation tensor is solved by a finite volume scheme. In order to obtain consistency, the space discretization of the divergence of the elastic part of the stress tensor in the momentum balance equation is derived using a weak form of the MAC scheme. For stability and accuracy purposes, the solution of the transport-reaction equation for the conformation tensor is split into pure convection steps, with a change of variable to the log-conformation tensor, and a reaction step, which consists in solving one ODE per cell via an Euler scheme with local sub-cycling. Numerical computations for the flow in the lid-driven cavity at Weissenberg numbers above one and the flow around a confined cylinder confirm the efficiency of the scheme.","PeriodicalId":50499,"journal":{"name":"Esaim-Mathematical Modelling and Numerical Analysis-Modelisation Mathematique et Analyse Numerique","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2023-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84377472","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
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