IMA Journal of Numerical Analysis最新文献_第6页

A mini immersed finite element method for two-phase Stokes problems on Cartesian meshes 笛卡尔网格上两相斯托克斯问题的微型沉浸式有限元方法

IF 2.1 2区数学

IMA Journal of Numerical Analysis Pub Date : 2024-09-09 DOI: 10.1093/imanum/drae053

Haifeng Ji, Dong Liang, Qian Zhang

{"title":"A mini immersed finite element method for two-phase Stokes problems on Cartesian meshes","authors":"Haifeng Ji, Dong Liang, Qian Zhang","doi":"10.1093/imanum/drae053","DOIUrl":"https://doi.org/10.1093/imanum/drae053","url":null,"abstract":"This paper presents a mini immersed finite element (IFE) method for solving two- and three-dimensional two-phase Stokes problems on Cartesian meshes. The IFE space is constructed from the conventional mini element, with shape functions modified on interface elements according to interface jump conditions while keeping the degrees of freedom unchanged. Both discontinuous viscosity coefficients and surface forces are taken into account in the construction. The interface is approximated using discrete level set functions, and explicit formulas for IFE basis functions and correction functions are derived, facilitating ease of implementation.The inf-sup stability and the optimal a priori error estimate of the IFE method, along with the optimal approximation capabilities of the IFE space, are derived rigorously, with constants that are independent of the mesh size and the manner in which the interface intersects the mesh, but may depend on the discontinuous viscosity coefficients. Additionally, it is proved that the condition number has the usual bound independent of the interface. Numerical experiments are provided to confirm the theoretical results.","PeriodicalId":56295,"journal":{"name":"IMA Journal of Numerical Analysis","volume":"82 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142160426","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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

New Banach spaces-based mixed finite element methods for the coupled poroelasticity and heat equations 基于巴拿赫空间的新混合有限元方法，用于耦合孔弹性方程和热方程

IF 2.1 2区数学

IMA Journal of Numerical Analysis Pub Date : 2024-09-05 DOI: 10.1093/imanum/drae052

Julio Careaga, Gabriel N Gatica, Cristian Inzunza, Ricardo Ruiz-Baier

{"title":"New Banach spaces-based mixed finite element methods for the coupled poroelasticity and heat equations","authors":"Julio Careaga, Gabriel N Gatica, Cristian Inzunza, Ricardo Ruiz-Baier","doi":"10.1093/imanum/drae052","DOIUrl":"https://doi.org/10.1093/imanum/drae052","url":null,"abstract":"In this paper, we introduce and analyze a Banach spaces-based approach yielding a fully-mixed finite element method for numerically solving the coupled poroelasticity and heat equations, which describe the interaction between the fields of deformation and temperature. A nonsymmetric pseudostress tensor is utilized to redefine the constitutive equation for the total stress, which is an extension of Hooke’s law to account for thermal effects. The resulting continuous formulation, posed in suitable Banach spaces, consists of a coupled system of three saddle point-type problems, each with right-hand terms that depend on data and the unknowns of the other two. The well-posedness of it is analyzed by means of a fixed-point strategy, so that the classical Banach theorem, along with the Babuška–Brezzi theory in Banach spaces, allows to conclude, under a smallness assumption on the data, the existence of a unique solution. The discrete analysis is conducted in a similar manner, utilizing the Brouwer and Banach theorems to demonstrate both the existence and uniqueness of the discrete solution. The rates of convergence of the resulting Galerkin method are then presented. Finally, a number of numerical tests are shown to validate the aforementioned statement and demonstrate the good performance of the method.","PeriodicalId":56295,"journal":{"name":"IMA Journal of Numerical Analysis","volume":"51 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142142448","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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

Necessary and sufficient conditions for avoiding Babuška’s paradox on simplicial meshes 在简单网格上避免巴布什卡悖论的必要条件和充分条件

IF 2.1 2区数学

IMA Journal of Numerical Analysis Pub Date : 2024-08-27 DOI: 10.1093/imanum/drae050

Sören Bartels, Philipp Tscherner

引用次数: 0

Computing Klein-Gordon Spectra 计算克莱因-戈登频谱

IF 2.1 2区数学

IMA Journal of Numerical Analysis Pub Date : 2024-08-26 DOI: 10.1093/imanum/drae032

Frank Rösler, Christiane Tretter

引用次数: 0

Mixed finite elements for the Gross–Pitaevskii eigenvalue problem: a priori error analysis and guaranteed lower energy bound 格罗斯-皮塔耶夫斯基特征值问题的混合有限元：先验误差分析和有保证的能量下限

IF 2.1 2区数学

IMA Journal of Numerical Analysis Pub Date : 2024-08-22 DOI: 10.1093/imanum/drae048

Dietmar Gallistl, Moritz Hauck, Yizhou Liang, Daniel Peterseim

引用次数: 0

Mass, momentum and energy preserving FEEC and broken-FEEC schemes for the incompressible Navier–Stokes equations 不可压缩纳维-斯托克斯方程的质量、动量和能量保全 FEEC 和破碎 FEEC 方案

IF 2.1 2区数学

IMA Journal of Numerical Analysis Pub Date : 2024-08-15 DOI: 10.1093/imanum/drae047

Valentin Carlier, Martin Campos Pinto, Francesco Fambri

{"title":"Mass, momentum and energy preserving FEEC and broken-FEEC schemes for the incompressible Navier–Stokes equations","authors":"Valentin Carlier, Martin Campos Pinto, Francesco Fambri","doi":"10.1093/imanum/drae047","DOIUrl":"https://doi.org/10.1093/imanum/drae047","url":null,"abstract":"In this article we propose two finite-element schemes for the Navier–Stokes equations, based on a reformulation that involves differential operators from the de Rham sequence and an advection operator with explicit skew-symmetry in weak form. Our first scheme is obtained by discretizing this formulation with conforming FEEC (Finite Element Exterior Calculus) spaces: it preserves the point-wise divergence free constraint of the velocity, its total momentum and its energy, in addition to being pressure robust. Following the broken-FEEC approach, our second scheme uses fully discontinuous spaces and local conforming projections to define the discrete differential operators. It preserves the same invariants up to a dissipation of energy to stabilize numerical discontinuities. For both schemes we use a middle point time discretization that preserve these invariants at the fully discrete level and we analyze its well-posedness in terms of a CFL condition. While our theoretical results hold for general finite elements preserving the de Rham structure, we consider one application to tensor-product spline spaces. Specifically, we conduct several numerical test cases to verify the high order accuracy of the resulting numerical methods, as well as their ability to handle general boundary conditions.","PeriodicalId":56295,"journal":{"name":"IMA Journal of Numerical Analysis","volume":"95 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-08-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141991902","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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

Numerical method and error estimate for stochastic Landau–Lifshitz–Bloch equation 随机 Landau-Lifshitz-Bloch 方程的数值方法和误差估计

IF 2.1 2区数学

IMA Journal of Numerical Analysis Pub Date : 2024-08-10 DOI: 10.1093/imanum/drae046

Beniamin Goldys, Chunxi Jiao, Kim-Ngan Le

引用次数: 0

On the fast convergence of minibatch heavy ball momentum 论小批重球动量的快速收敛

IF 2.1 2区数学

IMA Journal of Numerical Analysis Pub Date : 2024-08-09 DOI: 10.1093/imanum/drae033

Raghu Bollapragada, Tyler Chen, Rachel Ward

引用次数: 0

Long-term accuracy of numerical approximations of SPDEs with the stochastic Navier–Stokes equations as a paradigm 以随机纳维-斯托克斯方程为范例的 SPDE 数值近似的长期准确性

IF 2.1 2区数学

IMA Journal of Numerical Analysis Pub Date : 2024-07-16 DOI: 10.1093/imanum/drae043

Nathan E Glatt-Holtz, Cecilia F Mondaini

{"title":"Long-term accuracy of numerical approximations of SPDEs with the stochastic Navier–Stokes equations as a paradigm","authors":"Nathan E Glatt-Holtz, Cecilia F Mondaini","doi":"10.1093/imanum/drae043","DOIUrl":"https://doi.org/10.1093/imanum/drae043","url":null,"abstract":"This work introduces a general framework for establishing the long time accuracy for approximations of Markovian dynamical systems on separable Banach spaces. Our results illuminate the role that a certain uniformity in Wasserstein contraction rates for the approximating dynamics bears on long time accuracy estimates. In particular, our approach yields weak consistency bounds on ${mathbb{R}}^{+}$ while providing a means to sidestepping a commonly occurring situation where certain higher order moment bounds are unavailable for the approximating dynamics. Additionally, to facilitate the analytical core of our approach, we develop a refinement of certain ‘weak Harris theorems’. This extension expands the scope of applicability of such Wasserstein contraction estimates to a variety of interesting stochastic partial differential equation examples involving weaker dissipation or stronger nonlinearity than would be covered by the existing literature. As a guiding and paradigmatic example, we apply our formalism to the stochastic 2D Navier–Stokes equations and to a semi-implicit in time and spectral Galerkin in space numerical approximation of this system. In the case of a numerical approximation, we establish quantitative estimates on the approximation of invariant measures as well as prove weak consistency on ${mathbb{R}}^{+}$. To develop these numerical analysis results, we provide a refinement of $L^{2}_{x}$ accuracy bounds in comparison to the existing literature, which are results of independent interest.","PeriodicalId":56295,"journal":{"name":"IMA Journal of Numerical Analysis","volume":"64 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-07-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141631548","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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

The error bounds of Gaussian quadratures for one rational modification of Chebyshev measures 切比雪夫量纲的一次合理修正的高斯四则运算误差边界

IF 2.1 2区数学

IMA Journal of Numerical Analysis Pub Date : 2024-07-09 DOI: 10.1093/imanum/drae039

Rada M Mutavdžić Djukić

{"title":"The error bounds of Gaussian quadratures for one rational modification of Chebyshev measures","authors":"Rada M Mutavdžić Djukić","doi":"10.1093/imanum/drae039","DOIUrl":"https://doi.org/10.1093/imanum/drae039","url":null,"abstract":"For an analytic integrand, the error term in the Gaussian quadrature can be represented as a contour integral, where the contour is commonly taken to be an ellipse. Thus, finding its upper bound can be reduced to finding the maximum of the modulus of the kernel on the ellipse. The location of this maximum was investigated in many special cases, particularly, for the Gaussian quadrature with respect to the Chebyshev measures modified by a quadratic divisor (known as the Bernstein–Szeg̋ measures). Here, for the Gaussian quadratures with respect to the Chebyshev measures modified by a linear over linear rational factor, we examine the kernel and describe sufficient conditions for the maximum to occur on the real axis. Furthermore, an assessment of the kernel is made in each case, since in some cases the true maximum is hard to reach. Hence, we derive the error bounds for these quadrature formulas. The results are illustrated by the numerical examples. An alternative approach for estimating the error of the Gaussian quadrature with respect to the same measure can be found in [Djukić, D. L., Djukić, R. M. M., Reichel, L. & Spalević, M. M. (2023, Weighted averaged Gaussian quadrature rules for modified Chebyshev measure. Appl. Numer. Math., ISSN 0168-9274)].","PeriodicalId":56295,"journal":{"name":"IMA Journal of Numerical Analysis","volume":"51 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141566247","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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