Pub Date : 2023-03-01DOI: 10.1134/S1995423923010032
E. Klimova
{"title":"A Local Ensemble Data Assimilation Algorithm for Nonlinear Geophysical Models","authors":"E. Klimova","doi":"10.1134/S1995423923010032","DOIUrl":"https://doi.org/10.1134/S1995423923010032","url":null,"abstract":"","PeriodicalId":43697,"journal":{"name":"Numerical Analysis and Applications","volume":"16 1","pages":"22 - 33"},"PeriodicalIF":0.3,"publicationDate":"2023-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48191097","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-03-01DOI: 10.1134/S199542392301007X
O. V. Ushakova
{"title":"Realization of an Adaptation Criterion in Grid Generation Technology for Constructions Bounded by Surfaces of Revolution with Parallel Axes of Revolution1","authors":"O. V. Ushakova","doi":"10.1134/S199542392301007X","DOIUrl":"https://doi.org/10.1134/S199542392301007X","url":null,"abstract":"","PeriodicalId":43697,"journal":{"name":"Numerical Analysis and Applications","volume":"16 1","pages":"74 - 78"},"PeriodicalIF":0.3,"publicationDate":"2023-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45460126","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-03-01DOI: 10.1134/S1995423923010093
S. A. Gusev
{"title":"Erratum to: On the Variance of Estimation of a Diffusion Process Functional in a Domain with a Reflecting Boundary","authors":"S. A. Gusev","doi":"10.1134/S1995423923010093","DOIUrl":"https://doi.org/10.1134/S1995423923010093","url":null,"abstract":"","PeriodicalId":43697,"journal":{"name":"Numerical Analysis and Applications","volume":"16 1","pages":"91 - 91"},"PeriodicalIF":0.3,"publicationDate":"2023-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43294527","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-03-01DOI: 10.1134/S1995423923010019
O. S. Budnikova, M. N. Botoroeva, G. K. Sokolova
{"title":"Stability Domains of an Implicit Method for the Numerical Solution of Abel Type Integral Algebraic Equations","authors":"O. S. Budnikova, M. N. Botoroeva, G. K. Sokolova","doi":"10.1134/S1995423923010019","DOIUrl":"https://doi.org/10.1134/S1995423923010019","url":null,"abstract":"","PeriodicalId":43697,"journal":{"name":"Numerical Analysis and Applications","volume":"16 1","pages":"1 - 13"},"PeriodicalIF":0.3,"publicationDate":"2023-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47669507","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-03-01DOI: 10.1134/S1995423923010056
I. Kulikov, D. Karavaev
{"title":"A Piecewise-Parabolic Reconstruction of the Physical Variables in a Low-Dissipation HLL Method for the Numerical Solution of the Equations of Special Relativistic Hydrodynamics","authors":"I. Kulikov, D. Karavaev","doi":"10.1134/S1995423923010056","DOIUrl":"https://doi.org/10.1134/S1995423923010056","url":null,"abstract":"","PeriodicalId":43697,"journal":{"name":"Numerical Analysis and Applications","volume":"16 1","pages":"45 - 60"},"PeriodicalIF":0.3,"publicationDate":"2023-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43715089","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-03-01DOI: 10.1134/S1995423923010081
S. V. Cherdantsev, P. Shlapakov, S. I. Goloskokov, K. Lebedev, A. Erastov
{"title":"Unsteady Concentration Field of a Reacting Gas in the Vicinity of a Burning Coal Particle","authors":"S. V. Cherdantsev, P. Shlapakov, S. I. Goloskokov, K. Lebedev, A. Erastov","doi":"10.1134/S1995423923010081","DOIUrl":"https://doi.org/10.1134/S1995423923010081","url":null,"abstract":"","PeriodicalId":43697,"journal":{"name":"Numerical Analysis and Applications","volume":"16 1","pages":"79 - 90"},"PeriodicalIF":0.3,"publicationDate":"2023-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46195650","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-12-08DOI: 10.1134/s1995423922040097
M. Yu. Kokurin, V. V. Klyuchev
Abstract
M.M. Lavrentiev’s linear integral equation arises as a result of a special transformation of a nonlinear coefficient inverse wave sensing problem. The completeness of the set of products of regular harmonic functions and Newtonian potentials supported by a segment is proved. As a corollary, we establish the uniqueness of the solution to M.M. Lavrentiev’s equation and a related inverse problem of wave sensing. We present results of an approximate solution of this equation by using parallel calculations.
{"title":"Uniqueness Conditions and Numerical Approximation of the Solution to M. M. Lavrentiev’s Integral Equation","authors":"M. Yu. Kokurin, V. V. Klyuchev","doi":"10.1134/s1995423922040097","DOIUrl":"https://doi.org/10.1134/s1995423922040097","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>M.M. Lavrentiev’s linear integral equation arises as a result of a special transformation of a nonlinear coefficient inverse wave sensing problem. The completeness of the set of products of regular harmonic functions and Newtonian potentials supported by a segment is proved. As a corollary, we establish the uniqueness of the solution to M.M. Lavrentiev’s equation and a related inverse problem of wave sensing. We present results of an approximate solution of this equation by using parallel calculations.</p>","PeriodicalId":43697,"journal":{"name":"Numerical Analysis and Applications","volume":"83 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2022-12-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138528376","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-12-08DOI: 10.1134/s1995423922040012
A. K. Alekseev, A. E. Bondarev
Abstract
This paper deals with estimation of local (pointwise) approximation error on an ensemble of numerical solutions obtained by using independent algorithms. A variational inverse problem is posed for approximation error estimation. This problem is ill-posed due to translation-invariance of the governing equations. Zero order Tikhonov regularization is applied to obtain stable solutions. Numerical tests for two-dimensional equations describing inviscid compressible flow are performed to verify the efficiency of the algorithm. The approximation error estimates obtained by using the inverse problem are in satisfactory agreement with those obtained by Richardson extrapolation, but with significantly less computational costs.
{"title":"Estimation of Pointwise Approximation Error Using a Set of Numerical Solutions","authors":"A. K. Alekseev, A. E. Bondarev","doi":"10.1134/s1995423922040012","DOIUrl":"https://doi.org/10.1134/s1995423922040012","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>This paper deals with estimation of local (pointwise) approximation error on an ensemble of numerical solutions obtained by using independent algorithms. A variational inverse problem is posed for approximation error estimation. This problem is ill-posed due to translation-invariance of the governing equations. Zero order Tikhonov regularization is applied to obtain stable solutions. Numerical tests for two-dimensional equations describing inviscid compressible flow are performed to verify the efficiency of the algorithm. The approximation error estimates obtained by using the inverse problem are in satisfactory agreement with those obtained by Richardson extrapolation, but with significantly less computational costs.</p>","PeriodicalId":43697,"journal":{"name":"Numerical Analysis and Applications","volume":"32 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2022-12-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138528362","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-12-08DOI: 10.1134/s1995423922040061
S. Kamouche, H. Guebbai
Abstract
In this paper, we introduce a new convergence mode to deal with the generalized spectrum approximation of two bounded operators. This new technique is obtained by extending the well-known (nu)-convergence used in the case of classical spectrum approximation. This new vision allows us to see the (nu)-convergence assumption as a special case of our new method compared to the hypotheses needed in the old methods, those required in this paper are weaker. In addition, we prove that the property (U) holds, which solves a spectral pollution problem arising in the spectrum approximation of unbounded operators.
{"title":"New Convergence Mode For Generalized Spectrum Approximation","authors":"S. Kamouche, H. Guebbai","doi":"10.1134/s1995423922040061","DOIUrl":"https://doi.org/10.1134/s1995423922040061","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>In this paper, we introduce a new convergence mode to deal with the generalized spectrum approximation of two bounded operators. This new technique is obtained by extending the well-known <span>(nu)</span>-convergence used in the case of classical spectrum approximation. This new vision allows us to see the <span>(nu)</span>-convergence assumption as a special case of our new method compared to the hypotheses needed in the old methods, those required in this paper are weaker. In addition, we prove that the property <span>(U)</span> holds, which solves a spectral pollution problem arising in the spectrum approximation of unbounded operators.</p>","PeriodicalId":43697,"journal":{"name":"Numerical Analysis and Applications","volume":"54 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2022-12-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138528375","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-12-08DOI: 10.1134/s1995423922040036
M. Djaghout, A. Chaoui, K. Zennir
Abstract
This article discusses a mixed finite element method combined with the backward-Euler method to study the hyperbolic p–bi-Laplace equation, where the existence and uniqueness of solution for the discretized problem are shown in Lebesgue and Sobolev spaces. A mixed formulation and an inf-sup condition are then given to prove the well-posedness of the scheme and optimal a priori error estimates for fully discrete schemes are extracted. Finally, a numerical example is given to confirm the theoretical results obtained.
{"title":"On Discretization of the Evolution p-Bi-Laplace Equation","authors":"M. Djaghout, A. Chaoui, K. Zennir","doi":"10.1134/s1995423922040036","DOIUrl":"https://doi.org/10.1134/s1995423922040036","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>This article discusses a mixed finite element method combined with the backward-Euler method to study the hyperbolic <i>p</i>–bi-Laplace equation, where the existence and uniqueness of solution for the discretized problem are shown in Lebesgue and Sobolev spaces. A mixed formulation and an inf-sup condition are then given to prove the well-posedness of the scheme and optimal a priori error estimates for fully discrete schemes are extracted. Finally, a numerical example is given to confirm the theoretical results obtained.</p>","PeriodicalId":43697,"journal":{"name":"Numerical Analysis and Applications","volume":"1 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2022-12-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138528370","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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