Esaim-Mathematical Modelling and Numerical Analysis-Modelisation Mathematique et Analyse Numerique最新文献_第10页

A fully-mixed formulation in Banach spaces for the coupling of the steady Brinkman-Forchheimer and double-diffusion equations 稳定Brinkman-Forchheimer方程与双扩散方程耦合的Banach空间全混合公式

IF 1.9 3区数学

Esaim-Mathematical Modelling and Numerical Analysis-Modelisation Mathematique et Analyse Numerique Pub Date : 2021-10-29 DOI: 10.1051/m2an/2021072

Sergio Caucao, G. Gatica, J. Ortega

{"title":"A fully-mixed formulation in Banach spaces for the coupling of the steady Brinkman-Forchheimer and double-diffusion equations","authors":"Sergio Caucao, G. Gatica, J. Ortega","doi":"10.1051/m2an/2021072","DOIUrl":"https://doi.org/10.1051/m2an/2021072","url":null,"abstract":"We propose and analyze a new mixed finite element method for the nonlinear problem given by the coupling of the steady Brinkman--Forchheimer and double-diffusion equations. Besides the velocity, temperature, and concentration, our approach introduces the velocity gradient, the pseudostress tensor, and a pair of vectors involving the temperature/concentration, its gradient and the velocity, as further unknowns. As a consequence, we obtain a fully mixed variational formulation presenting a Banach spaces framework in each set of equations. In this way, and differently from the techniques previously developed for this and related coupled problems, no augmentation procedure needs to be incorporated now into the formulation nor into the solvability analysis. The resulting non-augmented scheme is then written equivalently as a fixed-point equation, so that the well-known Banach theorem, combined with classical results on nonlinear monotone operators and the Babusska-Brezzi theory in Banach spaces, are applied to prove the unique solvability of the continuous and discrete systems. Appropriate finite element subspaces satisfying the required discrete inf-sup conditions are specified, and optimal a priori error estimates are derived. Several numerical examples confirm the theoretical rates of convergence and illustrate the performance and flexibility of the method.","PeriodicalId":50499,"journal":{"name":"Esaim-Mathematical Modelling and Numerical Analysis-Modelisation Mathematique et Analyse Numerique","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2021-10-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88715966","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

Bloch waves in high contrast electromagnetic crystals 高对比度电磁晶体中的布洛赫波

IF 1.9 3区数学

Esaim-Mathematical Modelling and Numerical Analysis-Modelisation Mathematique et Analyse Numerique Pub Date : 2021-10-23 DOI: 10.1051/m2an/2022045

R. Lipton, Robert Viator, Silvia Jiménez Bolanos, A. Adili

引用次数: 2

A variational sheath model for gyrokinetic Vlasov-Poisson equations 陀螺动力学Vlasov-Poisson方程的变分鞘层模型

IF 1.9 3区数学

Esaim-Mathematical Modelling and Numerical Analysis-Modelisation Mathematique et Analyse Numerique Pub Date : 2021-10-08 DOI: 10.1051/m2an/2021067

M. Badsi, B. Després, M. Campos-Pinto, Ludovic Godard-Cadillac

引用次数: 0

Global existence of weak solutions to unsaturated poroelasticity 非饱和孔隙弹性问题弱解的整体存在性

IF 1.9 3区数学

Esaim-Mathematical Modelling and Numerical Analysis-Modelisation Mathematique et Analyse Numerique Pub Date : 2021-10-08 DOI: 10.1051/m2an/2021063

J. Both, Iuliu Sorin Pop, I. Yotov

{"title":"Global existence of weak solutions to unsaturated poroelasticity","authors":"J. Both, Iuliu Sorin Pop, I. Yotov","doi":"10.1051/m2an/2021063","DOIUrl":"https://doi.org/10.1051/m2an/2021063","url":null,"abstract":"We study unsaturated poroelasticity, i.e., coupled hydro-mechanical processes in variably saturated porous media, here modeled by a non-linear extension of Biot's well-known quasi-static consolidation model. The coupled elliptic-parabolic system of partial differential equations is a simplified version of the general model for multi-phase flow in deformable porous media, obtained under similar assumptions as usually considered for Richards' equation. In this work, existence of weak solutions is established in several steps involving a numerical approximation of the problem using a physically-motivated regularization and a finite element/finite volume discretization. Eventually, solvability of the original problem is proved by a combination of the Rothe and Galerkin methods, and further compactness arguments. This approach in particular provides the convergence of the numerical discretization to a regularized model for unsaturated poroelasticity. The final existence result holds under non-degeneracy conditions and natural continuity properties for the constitutive relations. The assumptions are demonstrated to be reasonable in view of geotechnical applications.","PeriodicalId":50499,"journal":{"name":"Esaim-Mathematical Modelling and Numerical Analysis-Modelisation Mathematique et Analyse Numerique","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2021-10-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80711520","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: 6

Finite element methods for the Darcy-Forchheimer problem coupled with the convection-diffusion-reaction problem 耦合对流-扩散-反应问题的Darcy-Forchheimer问题的有限元方法

IF 1.9 3区数学

Esaim-Mathematical Modelling and Numerical Analysis-Modelisation Mathematique et Analyse Numerique Pub Date : 2021-10-07 DOI: 10.1051/m2an/2021066

Toni Sayah, G. Semaan, Faouzi Triki

引用次数: 2

A virtual element discretization for the time dependent Navier-Stokes equations in stream-function formulation 流函数公式中含时Navier-Stokes方程的虚元离散化

IF 1.9 3区数学

Esaim-Mathematical Modelling and Numerical Analysis-Modelisation Mathematique et Analyse Numerique Pub Date : 2021-10-03 DOI: 10.1051/m2an/2021058

D. Adak, D. Mora, S. Natarajan, A. Silgado

引用次数: 11

Basic convergence theory for the network element method 网元法的基本收敛理论

IF 1.9 3区数学

Esaim-Mathematical Modelling and Numerical Analysis-Modelisation Mathematique et Analyse Numerique Pub Date : 2021-09-28 DOI: 10.1051/m2an/2021062

J. Coatléven

引用次数: 3

Structured coagulation-fragmentation equation in the space of radon measures: Unifying discrete and continuous models 氡测度空间中的结构化混凝破碎方程:统一离散和连续模型

IF 1.9 3区数学

Esaim-Mathematical Modelling and Numerical Analysis-Modelisation Mathematique et Analyse Numerique Pub Date : 2021-09-26 DOI: 10.1051/m2an/2021061

Azmy S. Ackleh, Rainey Lyons, N. Saintier

引用次数: 5

A Krylov subspace type method for Electrical Impedance Tomography 电阻抗层析成像的Krylov子空间型方法

IF 1.9 3区数学

Esaim-Mathematical Modelling and Numerical Analysis-Modelisation Mathematique et Analyse Numerique Pub Date : 2021-09-26 DOI: 10.1051/m2an/2021057

M. Pasha, Shyla Kupis, S. Ahmad, T. Khan

{"title":"A Krylov subspace type method for Electrical Impedance Tomography","authors":"M. Pasha, Shyla Kupis, S. Ahmad, T. Khan","doi":"10.1051/m2an/2021057","DOIUrl":"https://doi.org/10.1051/m2an/2021057","url":null,"abstract":"Electrical Impedance Tomography (EIT) is a well-known imaging technique for detecting the electrical properties of an object in order to detect anomalies, such as conductive or resistive targets. More specifically, EIT has many applications in medical imaging for the detection and location of bodily tumors since it is an affordable and non-invasive method, which aims to recover the internal conductivity of a body using voltage measurements resulting from applying low frequency current at electrodes placed at its surface.\u0000\u0000Mathematically, the reconstruction of the internal conductivity is a severely ill-posed inverse problem and yields a poor quality image reconstruction. To remedy this difficulty, at least in part, we regularize and solve the nonlinear minimization problem by the aid of a Krylov subspace-type method for the linear sub problem during each iteration. In EIT, a tumor or general anomaly can be modeled as a piecewise constant perturbation of a smooth background, hence, we solve the regularized problem on a subspace of relatively small dimension by the Flexible Golub-Kahan process that provides solutions that have sparse representation. For comparison, we use a well-known modified Gauss-Newton algorithm as a benchmark. Using simulations, we demonstrate the effectiveness of the proposed method. The obtained reconstructions indicate that the Krylov subspace method is better adapted to solve the ill-posed EIT problem and results in higher resolution images and faster convergence compared to reconstructions using the modified Gauss-Newton algorithm.","PeriodicalId":50499,"journal":{"name":"Esaim-Mathematical Modelling and Numerical Analysis-Modelisation Mathematique et Analyse Numerique","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2021-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83167036","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

An embedded discontinuous Galerkin method for the Oseen equations Oseen方程的嵌入不连续伽辽金法

IF 1.9 3区数学

Esaim-Mathematical Modelling and Numerical Analysis-Modelisation Mathematique et Analyse Numerique Pub Date : 2021-09-21 DOI: 10.1051/m2an/2021059

Yongbin Han, Yanren Hou

引用次数: 1