Pub Date : 2023-10-08DOI: 10.1007/s10092-023-00542-4
Ivo Dravins, Maya Neytcheva
Abstract We consider the iterative solution of algebraic systems, arising in optimal control problems constrained by a partial differential equation with additional box constraints on the state and the control variables, and sparsity imposed on the control. A nonsymmetric two-by-two block preconditioner is analysed and tested for a wide range of problem, regularization and discretization parameters. The constraint equation characterizes convection-diffusion processes.
{"title":"Preconditioning of discrete state- and control-constrained optimal control convection-diffusion problems","authors":"Ivo Dravins, Maya Neytcheva","doi":"10.1007/s10092-023-00542-4","DOIUrl":"https://doi.org/10.1007/s10092-023-00542-4","url":null,"abstract":"Abstract We consider the iterative solution of algebraic systems, arising in optimal control problems constrained by a partial differential equation with additional box constraints on the state and the control variables, and sparsity imposed on the control. A nonsymmetric two-by-two block preconditioner is analysed and tested for a wide range of problem, regularization and discretization parameters. The constraint equation characterizes convection-diffusion processes.","PeriodicalId":9522,"journal":{"name":"Calcolo","volume":"2016 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135198276","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}
Pub Date : 2023-10-06DOI: 10.1007/s10092-023-00541-5
Naresh Kumar, Bhupen Deka
{"title":"A numerical method for analysis and simulation of diffusive viscous wave equations with variable coefficients on polygonal meshes","authors":"Naresh Kumar, Bhupen Deka","doi":"10.1007/s10092-023-00541-5","DOIUrl":"https://doi.org/10.1007/s10092-023-00541-5","url":null,"abstract":"","PeriodicalId":9522,"journal":{"name":"Calcolo","volume":"11 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135346594","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}
Pub Date : 2023-09-23DOI: 10.1007/s10092-023-00539-z
Sudheer Mishra, E. Natarajan
{"title":"A streamline-derivative-based local projection stabilization virtual element method for nonlinear convection–diffusion–reaction equation","authors":"Sudheer Mishra, E. Natarajan","doi":"10.1007/s10092-023-00539-z","DOIUrl":"https://doi.org/10.1007/s10092-023-00539-z","url":null,"abstract":"","PeriodicalId":9522,"journal":{"name":"Calcolo","volume":"2014 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135966340","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}
Pub Date : 2023-09-12DOI: 10.1007/s10092-023-00540-6
Deepika Garg, Sashikumaar Ganesan
Abstract An a priori analysis for generalized local projection stabilized finite element approximations for the solution of an advection–reaction equation is presented in this article. The stability and a priori error estimates are derived for the conforming, and nonconforming (Crouzeix–Raviart) approximations in the local projection streamline derivative norm. Finally, the validation of the proposed stabilization scheme and verification of the derived estimates are presented with appropriate numerical experiments.
{"title":"Local projection stabilized finite element methods for advection–reaction problems","authors":"Deepika Garg, Sashikumaar Ganesan","doi":"10.1007/s10092-023-00540-6","DOIUrl":"https://doi.org/10.1007/s10092-023-00540-6","url":null,"abstract":"Abstract An a priori analysis for generalized local projection stabilized finite element approximations for the solution of an advection–reaction equation is presented in this article. The stability and a priori error estimates are derived for the conforming, and nonconforming (Crouzeix–Raviart) approximations in the local projection streamline derivative norm. Finally, the validation of the proposed stabilization scheme and verification of the derived estimates are presented with appropriate numerical experiments.","PeriodicalId":9522,"journal":{"name":"Calcolo","volume":"40 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135826814","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}
Pub Date : 2023-08-24DOI: 10.1007/s10092-023-00538-0
Shangyou Zhang
{"title":"A macro-bubble enriched P1–P0 finite element for the Stokes equations on triangular and tetrahedral meshes","authors":"Shangyou Zhang","doi":"10.1007/s10092-023-00538-0","DOIUrl":"https://doi.org/10.1007/s10092-023-00538-0","url":null,"abstract":"","PeriodicalId":9522,"journal":{"name":"Calcolo","volume":" ","pages":""},"PeriodicalIF":1.7,"publicationDate":"2023-08-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46996442","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}
Pub Date : 2023-08-05DOI: 10.1007/s10092-023-00537-1
Phung Van Manh
{"title":"Conditioning of Fourier sums on a quadratic curve","authors":"Phung Van Manh","doi":"10.1007/s10092-023-00537-1","DOIUrl":"https://doi.org/10.1007/s10092-023-00537-1","url":null,"abstract":"","PeriodicalId":9522,"journal":{"name":"Calcolo","volume":" ","pages":""},"PeriodicalIF":1.7,"publicationDate":"2023-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47421542","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}
Pub Date : 2023-07-28DOI: 10.1007/s10092-023-00535-3
Xiangyun Meng, M. Stynes
{"title":"Energy-norm and balanced-norm supercloseness error analysis of a finite volume method on Shishkin meshes for singularly perturbed reaction–diffusion problems","authors":"Xiangyun Meng, M. Stynes","doi":"10.1007/s10092-023-00535-3","DOIUrl":"https://doi.org/10.1007/s10092-023-00535-3","url":null,"abstract":"","PeriodicalId":9522,"journal":{"name":"Calcolo","volume":" ","pages":""},"PeriodicalIF":1.7,"publicationDate":"2023-07-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48764802","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}
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