Pub Date : 2023-06-01DOI: 10.4208/nmtma.oa-2023-0082
Alessia Del Grosso, Manuel J. Castro Díaz, Christophe Chalons and Tomás Morales de Luna
{"title":"On Lagrange-Projection Schemes for Shallow Water Flows Over Movable Bottom with Suspended and Bedload Transport","authors":"Alessia Del Grosso, Manuel J. Castro Díaz, Christophe Chalons and Tomás Morales de Luna","doi":"10.4208/nmtma.oa-2023-0082","DOIUrl":"https://doi.org/10.4208/nmtma.oa-2023-0082","url":null,"abstract":"","PeriodicalId":50225,"journal":{"name":"Journal of Computational Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135194185","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}
Pub Date : 2023-06-01DOI: 10.4208/jcm.2211-m2021-0255
Y. Qian, Fei Wang and Wenjing Yan
In this paper, we introduce and analyze an augmented mixed discontinuous Galerkin (MDG) method for a class of quasi-Newtonian Stokes flows. In the mixed formulation, the unknowns are strain rate, stress and velocity, which are approximated by a discontinuous piecewise polynomial triplet P S k +1 - P S k +1 - P k for k ≥ 0. Here, the discontinuous piecewise polynomial function spaces for the field of strain rate and the stress field are designed to be symmetric. In addition, the pressure is easily recovered through simple postprocessing. For the benefit of the analysis, we enrich the MDG scheme with the constitutive equation relating the stress and the strain rate, so that the well-posedness of the augmented formulation is obtained by a nonlinear functional analysis. For k ≥ 0, we get the optimal convergence order for the stress in broken H ( div )-norm and velocity in L 2 -norm. Furthermore, the error estimates of the strain rate and the stress in L 2 -norm, and the pressure in L 2 -norm are optimal under certain conditions. Finally, several numerical examples are given to show the performance of the augmented MDG method and verify the theoretical results. Numerical evidence is provided to show that the orders of convergence are sharp
{"title":"Mixed Discontinuous Galerkin Method for Quasi-Newtonian Stokes Flows","authors":"Y. Qian, Fei Wang and Wenjing Yan","doi":"10.4208/jcm.2211-m2021-0255","DOIUrl":"https://doi.org/10.4208/jcm.2211-m2021-0255","url":null,"abstract":"In this paper, we introduce and analyze an augmented mixed discontinuous Galerkin (MDG) method for a class of quasi-Newtonian Stokes flows. In the mixed formulation, the unknowns are strain rate, stress and velocity, which are approximated by a discontinuous piecewise polynomial triplet P S k +1 - P S k +1 - P k for k ≥ 0. Here, the discontinuous piecewise polynomial function spaces for the field of strain rate and the stress field are designed to be symmetric. In addition, the pressure is easily recovered through simple postprocessing. For the benefit of the analysis, we enrich the MDG scheme with the constitutive equation relating the stress and the strain rate, so that the well-posedness of the augmented formulation is obtained by a nonlinear functional analysis. For k ≥ 0, we get the optimal convergence order for the stress in broken H ( div )-norm and velocity in L 2 -norm. Furthermore, the error estimates of the strain rate and the stress in L 2 -norm, and the pressure in L 2 -norm are optimal under certain conditions. Finally, several numerical examples are given to show the performance of the augmented MDG method and verify the theoretical results. Numerical evidence is provided to show that the orders of convergence are sharp","PeriodicalId":50225,"journal":{"name":"Journal of Computational Mathematics","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44270859","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}
Pub Date : 2023-06-01DOI: 10.4208/jcm.2301-m2021-0313
Debora Cores and Johanna Figueroa
{"title":"A Low-Cost Optimization Approach for Solving Minimum Norm Linear Systems and Linear Least-Squares Problems","authors":"Debora Cores and Johanna Figueroa","doi":"10.4208/jcm.2301-m2021-0313","DOIUrl":"https://doi.org/10.4208/jcm.2301-m2021-0313","url":null,"abstract":"","PeriodicalId":50225,"journal":{"name":"Journal of Computational Mathematics","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43089056","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}
Pub Date : 2023-06-01DOI: 10.4208/jcm.2211-m2022-0186
Lexing Ying
{"title":"Double Flip Move for Ising Models with Mixed Boundary Conditions","authors":"Lexing Ying","doi":"10.4208/jcm.2211-m2022-0186","DOIUrl":"https://doi.org/10.4208/jcm.2211-m2022-0186","url":null,"abstract":"","PeriodicalId":50225,"journal":{"name":"Journal of Computational Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135525293","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}
Pub Date : 2023-06-01DOI: 10.4208/nmtma.oa-2022-0203
Luisa D'Amore
{"title":"Space-Time Decomposition of Kalman Filter","authors":"Luisa D'Amore","doi":"10.4208/nmtma.oa-2022-0203","DOIUrl":"https://doi.org/10.4208/nmtma.oa-2022-0203","url":null,"abstract":"","PeriodicalId":50225,"journal":{"name":"Journal of Computational Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135144241","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}
{"title":"HRW: Hybrid Residual and Weak Form Loss for Solving Elliptic Interface Problems with Neural Network","authors":"Muzhou Hou, Yinghao Chen, Shen Cao, Yuntian Chen and Jinyong Ying","doi":"10.4208/nmtma.oa-2023-0097","DOIUrl":"https://doi.org/10.4208/nmtma.oa-2023-0097","url":null,"abstract":"","PeriodicalId":50225,"journal":{"name":"Journal of Computational Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135194756","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}
Pub Date : 2023-05-01DOI: 10.4208/jcm.2206-m2021-0240
T. Sun, Chengjian Sun
This paper deals with numerical methods for solving one-dimensional (1D) and two-dimensional (2D) initial-boundary value problems (IBVPs) of space-fractional sine-Gordon equations (SGEs) with distributed delay. For 1D problems, we construct a kind of one-parameter finite difference (OPFD) method. It is shown that, under a suitable condition, the proposed method is convergent with second order accuracy both in time and space. In implementation, the preconditioned conjugate gradient (PCG) method with the Strang circulant preconditioner is carried out to improve the computational efficiency of the OPFD method. For 2D problems, we develop another kind of OPFD method. For such a method, two classes of accelerated schemes are suggested, one is alternative direction implicit (ADI) scheme and the other is ADI-PCG scheme. In particular, we prove that ADI scheme can arrive at second-order accuracy in time and space. With some numerical experiments, the computational effectiveness and accuracy of the methods are further verified. Moreover, for the suggested methods, a numerical comparison in computational efficiency is presented.
{"title":"One-Parameter Finite Difference Methods and Their Accelerated Schemes for Space-Fractional Sine-Gordon Equations with Distributed Delay","authors":"T. Sun, Chengjian Sun","doi":"10.4208/jcm.2206-m2021-0240","DOIUrl":"https://doi.org/10.4208/jcm.2206-m2021-0240","url":null,"abstract":"This paper deals with numerical methods for solving one-dimensional (1D) and two-dimensional (2D) initial-boundary value problems (IBVPs) of space-fractional sine-Gordon equations (SGEs) with distributed delay. For 1D problems, we construct a kind of one-parameter finite difference (OPFD) method. It is shown that, under a suitable condition, the proposed method is convergent with second order accuracy both in time and space. In implementation, the preconditioned conjugate gradient (PCG) method with the Strang circulant preconditioner is carried out to improve the computational efficiency of the OPFD method. For 2D problems, we develop another kind of OPFD method. For such a method, two classes of accelerated schemes are suggested, one is alternative direction implicit (ADI) scheme and the other is ADI-PCG scheme. In particular, we prove that ADI scheme can arrive at second-order accuracy in time and space. With some numerical experiments, the computational effectiveness and accuracy of the methods are further verified. Moreover, for the suggested methods, a numerical comparison in computational efficiency is presented.","PeriodicalId":50225,"journal":{"name":"Journal of Computational Mathematics","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2023-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46489530","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}
Pub Date : 2023-05-01DOI: 10.4208/jcm.2212-m2021-0231
Yuping Zeng, M. Zhong
A mixed finite element method is presented for the Biot consolidation problem in poroe-lasticity. More precisely, the displacement is approximated by using the Crouzeix-Raviart nonconforming finite elements, while the fluid pressure is approximated by using the node conforming finite elements. The well-posedness of the fully discrete scheme is established, and a corresponding priori error estimate with optimal order in the energy norm is also derived. Numerical experiments are provided to validate the theoretical results. Mathematics
{"title":"A Coupled Method Combining Crouzeix-Raviart Nonconforming and Node Conforming Finite Element Spaces for Boit Consolidation Model","authors":"Yuping Zeng, M. Zhong","doi":"10.4208/jcm.2212-m2021-0231","DOIUrl":"https://doi.org/10.4208/jcm.2212-m2021-0231","url":null,"abstract":"A mixed finite element method is presented for the Biot consolidation problem in poroe-lasticity. More precisely, the displacement is approximated by using the Crouzeix-Raviart nonconforming finite elements, while the fluid pressure is approximated by using the node conforming finite elements. The well-posedness of the fully discrete scheme is established, and a corresponding priori error estimate with optimal order in the energy norm is also derived. Numerical experiments are provided to validate the theoretical results. Mathematics","PeriodicalId":50225,"journal":{"name":"Journal of Computational Mathematics","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2023-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42854561","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}
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