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Galerkin Finite Element Approximation for Semilinear Stochastic Time-Tempered Fractional Wave Equations with Multiplicative Gaussian Noise and Additive Fractional Gaussian Noise 具有乘性高斯噪声和加性分数阶高斯噪声的半线性随机时变分数波方程的Galerkin有限元逼近
IF 1.3 4区 数学
Numerical Mathematics-Theory Methods and Applications Pub Date : 2022-06-01 DOI: 10.4208/nmtma.oa-2022-0013s
Yajing Li, Yejuan Wang, W. Deng, Daxin Nie
{"title":"Galerkin Finite Element Approximation for Semilinear Stochastic Time-Tempered Fractional Wave Equations with Multiplicative Gaussian Noise and Additive Fractional Gaussian Noise","authors":"Yajing Li, Yejuan Wang, W. Deng, Daxin Nie","doi":"10.4208/nmtma.oa-2022-0013s","DOIUrl":"https://doi.org/10.4208/nmtma.oa-2022-0013s","url":null,"abstract":". To model wave propagation in inhomogeneous media with frequency de-pendent power-law attenuation, it is needed to use the fractional powers of symmetric coercive elliptic operators in space and the Caputo tempered fractional derivative in time. The model studied in this paper is semilinear stochastic space-time fractional wave equations driven by infinite dimensional multiplicative Gaussian noise and additive fractional Gaussian noise, because of the potential fluctuations of the external sources. The purpose of this work is to discuss the Galerkin finite element approximation for the semilinear stochastic fractional wave equation. First, the space-time multiplicative Gaussian noise and additive fractional Gaussian noise are discretized, which results in a regularized stochastic fractional wave equation while introducing a modeling error in the mean-square sense. We further present a complete regularity theory for the regularized equation. A standard finite element approximation is used for the spatial operator, and a mean-square priori estimates for the modeling error and the approximation error to the solution of the regularized problem are established. Finally, numerical experiments are performed to confirm the theoretical analysis.","PeriodicalId":51146,"journal":{"name":"Numerical Mathematics-Theory Methods and Applications","volume":" ","pages":""},"PeriodicalIF":1.3,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47559120","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Dual Control Methods for a Mixed Control Problem with Optimal Stopping Arising in Optimal Consumption and Investment 最优消费和投资中出现最优停止的混合控制问题的对偶控制方法
IF 1.3 4区 数学
Numerical Mathematics-Theory Methods and Applications Pub Date : 2022-06-01 DOI: 10.4208/nmtma.oa-2022-0001
Jingtang Ma, Jie Xing, Shande Yang
{"title":"Dual Control Methods for a Mixed Control Problem with Optimal Stopping Arising in Optimal Consumption and Investment","authors":"Jingtang Ma, Jie Xing, Shande Yang","doi":"10.4208/nmtma.oa-2022-0001","DOIUrl":"https://doi.org/10.4208/nmtma.oa-2022-0001","url":null,"abstract":"","PeriodicalId":51146,"journal":{"name":"Numerical Mathematics-Theory Methods and Applications","volume":" ","pages":""},"PeriodicalIF":1.3,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48644542","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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 Immersed Interface Hybridized Difference Method for Parabolic Interface Problems 抛物界面问题的浸入界面杂交差分法
IF 1.3 4区 数学
Numerical Mathematics-Theory Methods and Applications Pub Date : 2022-06-01 DOI: 10.4208/nmtma.oa-2021-0154
Youngmok Jeon null, Son-Young Yi
{"title":"The Immersed Interface Hybridized Difference Method for Parabolic Interface Problems","authors":"Youngmok Jeon null, Son-Young Yi","doi":"10.4208/nmtma.oa-2021-0154","DOIUrl":"https://doi.org/10.4208/nmtma.oa-2021-0154","url":null,"abstract":"We propose several immersed interface hybridized difference methods (IHDMs), combined with the Crank-Nicolson time-stepping scheme, for parabolic interface problems. The IHDM is the same as the hybrid difference method away from the interface cells, but the finite difference operators on the interface cells are modified to maintain the same accuracy throughout the entire domain. For the modification process, we consider virtual extensions of two sub-solutions in the interface cells in such a way that they satisfy certain jump equations between them. We propose several different sets of jump equations and their resulting discrete methods for oneand two-dimensional problems. Some numerical results are presented to demonstrate the accuracy and robustness of the proposed methods. AMS subject classifications: 65N30, 65N38, 65N50","PeriodicalId":51146,"journal":{"name":"Numerical Mathematics-Theory Methods and Applications","volume":" ","pages":""},"PeriodicalIF":1.3,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43350569","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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 Survey of the L1 Scheme in the Discretisation of Time-Fractional Problems 时间分数问题离散化中的L1格式综述
IF 1.3 4区 数学
Numerical Mathematics-Theory Methods and Applications Pub Date : 2022-06-01 DOI: 10.4208/nmtma.oa-2022-0009s
M. Stynes
{"title":"A Survey of the L1 Scheme in the Discretisation of Time-Fractional Problems","authors":"M. Stynes","doi":"10.4208/nmtma.oa-2022-0009s","DOIUrl":"https://doi.org/10.4208/nmtma.oa-2022-0009s","url":null,"abstract":"","PeriodicalId":51146,"journal":{"name":"Numerical Mathematics-Theory Methods and Applications","volume":" ","pages":""},"PeriodicalIF":1.3,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42126327","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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: 25
A Third Order Accurate in Time, BDF-Type Energy Stable Scheme for the Cahn-Hilliard Equation Cahn-Hilliard方程的三阶时间精确BDF型能量稳定格式
IF 1.3 4区 数学
Numerical Mathematics-Theory Methods and Applications Pub Date : 2022-06-01 DOI: 10.4208/nmtma.oa-2021-0165
Kelong Cheng, Cheng Wang, S. Null, Yanmei Wu
{"title":"A Third Order Accurate in Time, BDF-Type Energy Stable Scheme for the Cahn-Hilliard Equation","authors":"Kelong Cheng, Cheng Wang, S. Null, Yanmei Wu","doi":"10.4208/nmtma.oa-2021-0165","DOIUrl":"https://doi.org/10.4208/nmtma.oa-2021-0165","url":null,"abstract":". In this paper we propose and analyze a backward differentiation formula (BDF) type numerical scheme for the Cahn-Hilliard equation with third order temporal accuracy. The Fourier pseudo-spectral method is used to discretize space. The surface diffusion and the nonlinear chemical potential terms are treated implicitly, while the expansive term is approximated by a third order explicit extrapolation formula for the sake of solvability. In addition, a third order accurate Douglas-Dupont regularization term, in the form of − A 0 ∆ t 2 ∆ N ( φ n +1 − φ n ) , is added in the numerical scheme. In particular, the energy stability is carefully derived in a modified version, so that a uniform bound for the original energy functional is available, and a theoretical justification of the coefficient A becomes available. As a result of this energy stability analysis, a uniform-in-time L 6 N bound of the numerical solution is obtained. And also, the optimal rate convergence analysis and error estimate are provided, in the L ∞ ∆ t (0 , T ; L 2 N ) ∩ L 2∆ t (0 , T ; H 2 h ) norm, with the help of the L 6 N bound for the numerical solution. A few numerical simulation results are presented to demonstrate the efficiency of the numerical scheme and the third order convergence.","PeriodicalId":51146,"journal":{"name":"Numerical Mathematics-Theory Methods and Applications","volume":" ","pages":""},"PeriodicalIF":1.3,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48105938","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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: 7
A Dual-Horizon Nonlocal Diffusion Model and Its Finite Element Discretization 双视界非局部扩散模型及其有限元离散化
IF 1.3 4区 数学
Numerical Mathematics-Theory Methods and Applications Pub Date : 2022-06-01 DOI: 10.4208/nmtma.oa-2022-0004s
Mingchao Bi, Lili Ju null, H. Tian
{"title":"A Dual-Horizon Nonlocal Diffusion Model and Its Finite Element Discretization","authors":"Mingchao Bi, Lili Ju null, H. Tian","doi":"10.4208/nmtma.oa-2022-0004s","DOIUrl":"https://doi.org/10.4208/nmtma.oa-2022-0004s","url":null,"abstract":". In this paper, we present a dual-horizon nonlocal diffusion model, in which the influence area at each point consists of a standard sphere horizon and an irregular dual horizon and its geometry is determined by the distribution of the varying horizon parameter. We prove the mass conservation and maximum principle of the proposed nonlocal model, and establish its well-posedness and convergence to the classical diffusion model. Noticing that the dual horizon-related term in fact vanishes in the corresponding variational form of the model, we then propose a finite element discretization for its numerical solution, which avoids the difficulty of accurate calculations of integrals on irregular intersection regions between the mesh elements and the dual horizons. Various numerical experiments in two and three dimensions are also performed to illustrate the usage of the variable horizon and demonstrate the effectiveness of the numerical scheme.","PeriodicalId":51146,"journal":{"name":"Numerical Mathematics-Theory Methods and Applications","volume":" ","pages":""},"PeriodicalIF":1.3,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43838960","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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 Discontinuous Galerkin Method by Divergence-Free Patch Reconstruction for Stokes Eigenvalue Problems Stokes特征值问题的无散度斑块重构不连续Galerkin方法
IF 1.3 4区 数学
Numerical Mathematics-Theory Methods and Applications Pub Date : 2022-06-01 DOI: 10.4208/nmtma.oa-2021-0085
Di Li, Z. Sun, Fengru Wang null, J. Yang
{"title":"The Discontinuous Galerkin Method by Divergence-Free Patch Reconstruction for Stokes Eigenvalue Problems","authors":"Di Li, Z. Sun, Fengru Wang null, J. Yang","doi":"10.4208/nmtma.oa-2021-0085","DOIUrl":"https://doi.org/10.4208/nmtma.oa-2021-0085","url":null,"abstract":"The discontinuous Galerkin method by divergence-free patch reconstruction is proposed for Stokes eigenvalue problems. It utilizes the mixed finite element framework. The patch reconstruction technique constructs two categories of approximation spaces. Namely, the local divergence-free space is employed to discretize the velocity space, and the pressure space is approximated by standard reconstruction space simultaneously. Benefit from the divergence-free constraint; the identical element patch serves two approximation spaces while using the element pair P/P. The optimal error estimate is derived under the inf-sup condition framework. Numerical examples are carried out to validate the inf-sup test and the theoretical results. AMS subject classifications: 49N45, 65N21","PeriodicalId":51146,"journal":{"name":"Numerical Mathematics-Theory Methods and Applications","volume":" ","pages":""},"PeriodicalIF":1.3,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41522140","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Hierarchical Absorbing Interface Conditions for Wave Propagation on Non-Uniform Meshes 波浪在非均匀网格上传播的分层吸收界面条件
IF 1.3 4区 数学
Numerical Mathematics-Theory Methods and Applications Pub Date : 2022-06-01 DOI: 10.4208/nmtma.oa-2021-0135
Shuyang Dai, Z. Sun, Fengru Wang, Jerry Zhijian Yang null, Cheng Yuan
{"title":"Hierarchical Absorbing Interface Conditions for Wave Propagation on Non-Uniform Meshes","authors":"Shuyang Dai, Z. Sun, Fengru Wang, Jerry Zhijian Yang null, Cheng Yuan","doi":"10.4208/nmtma.oa-2021-0135","DOIUrl":"https://doi.org/10.4208/nmtma.oa-2021-0135","url":null,"abstract":"In this paper, we propose hierarchical absorbing interface conditions to solve the problem of wave propagation in domains with a non-uniform space discretization or grid size inhomogeneity using Padé Via Lanczos (PVL) method. The proposed interface conditions add an auxiliary variable in the wave system to eliminate the spurious reflection at the interface between regions with different mesh sizes. The auxiliary variable with proper boundary condition can suppress the spurious reflection by cancelling the boundary source term produced by the space inhomogeneity in variational perspective. The new hierarchical interface conditions with the help of PVL implementation can effectively reduce the degree of freedom in solving the wave propagation problem. AMS subject classifications: 65K10, 65N22, 35L05","PeriodicalId":51146,"journal":{"name":"Numerical Mathematics-Theory Methods and Applications","volume":" ","pages":""},"PeriodicalIF":1.3,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42214553","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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 and Accurate Numerical Methods Using the Accelerated Spectral Deferred Correction for Solving Fractional Differential Equations 利用加速谱延迟校正求解分数阶微分方程的高效精确数值方法
IF 1.3 4区 数学
Numerical Mathematics-Theory Methods and Applications Pub Date : 2022-06-01 DOI: 10.4208/nmtma.oa-2022-0012s
Xuejuan Chen, Zhiping Mao null, G. Karniadakis
{"title":"Efficient and Accurate Numerical Methods Using the Accelerated Spectral Deferred Correction for Solving Fractional Differential Equations","authors":"Xuejuan Chen, Zhiping Mao null, G. Karniadakis","doi":"10.4208/nmtma.oa-2022-0012s","DOIUrl":"https://doi.org/10.4208/nmtma.oa-2022-0012s","url":null,"abstract":"","PeriodicalId":51146,"journal":{"name":"Numerical Mathematics-Theory Methods and Applications","volume":" ","pages":""},"PeriodicalIF":1.3,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42231635","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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 Hybrid Scheme of Level Set and Diffuse Interface Methods for Simulating Multi-Phase Compressible Flows 模拟多相可压缩流的水平集和扩散界面混合方法
IF 1.3 4区 数学
Numerical Mathematics-Theory Methods and Applications Pub Date : 2022-06-01 DOI: 10.4208/nmtma.oa-2021-0162
Mei Fu, Tiao Lu
{"title":"A Hybrid Scheme of Level Set and Diffuse Interface Methods for Simulating Multi-Phase Compressible Flows","authors":"Mei Fu, Tiao Lu","doi":"10.4208/nmtma.oa-2021-0162","DOIUrl":"https://doi.org/10.4208/nmtma.oa-2021-0162","url":null,"abstract":"","PeriodicalId":51146,"journal":{"name":"Numerical Mathematics-Theory Methods and Applications","volume":" ","pages":""},"PeriodicalIF":1.3,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48367280","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
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