Two-grid virtual element discretization of quasilinear elliptic problem
In this paper a two grid algorithm for quasilinear elliptic problem based on virtual element method (VEM) discretization is proposed. With this new algorithm the solution of a quasilinear elliptic problem on a fine grid is reduced to the solution of a quasilinear elliptic problem on a much coarser g...
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| Published in: | Mathematical modelling and analysis Vol. 29; no. 1; pp. 77 - 89 |
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| Main Authors: | , , |
| Format: | Journal Article |
| Language: | English |
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Vilnius Gediminas Technical University
23.02.2024
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| ISSN: | 1392-6292, 1648-3510 |
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| Abstract | In this paper a two grid algorithm for quasilinear elliptic problem based on virtual element method (VEM) discretization is proposed. With this new algorithm the solution of a quasilinear elliptic problem on a fine grid is reduced to the solution of a quasilinear elliptic problem on a much coarser grid, and the solution of a linear system on the fine grid. A priori error estimate in H1 norm is derived. Numerical experiments are carried out to illustrate the theoretical findings. |
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| AbstractList | In this paper a two grid algorithm for quasilinear elliptic problem based on virtual element method (VEM) discretization is proposed. With this new algorithm the solution of a quasilinear elliptic problem on a fine grid is reduced to the solution of a quasilinear elliptic problem on a much coarser grid, and the solution of a linear system on the fine grid. A priori error estimate in H1 norm is derived. Numerical experiments are carried out to illustrate the theoretical findings. In this paper a two grid algorithm for quasilinear elliptic problem based on virtual element method (VEM) discretization is proposed. With this new algorithm the solution of a quasilinear elliptic problem on a fine grid is reduced to the solution of a quasilinear elliptic problem on a much coarser grid, and the solution of a linear system on the fine grid. A priori error estimate in H1 norm is derived. Numerical experiments are carried out to illustrate the theoretical findings. Keywords: virtual element method, two grid algorithm, a priori error estimate. AMS Subject Classification: 65N30. |
| Audience | Academic |
| Author | Yang, Minghui Zhou, Zhaojie Chen, Fengxin |
| Author_xml | – sequence: 1 givenname: Fengxin surname: Chen fullname: Chen, Fengxin organization: School of Science, Shandong Jiaotong University, 250357 Jinan, China – sequence: 2 givenname: Minghui orcidid: 0009-0008-3960-2451 surname: Yang fullname: Yang, Minghui organization: School of Mathematics and Statistics, Shandong Normal University, 250014 Jinan, China – sequence: 3 givenname: Zhaojie surname: Zhou fullname: Zhou, Zhaojie organization: School of Mathematics and Statistics, Shandong Normal University, 250014 Jinan, China |
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| SubjectTerms | a priori error estimate Algorithms Approximation Discretization Error analysis Finite element analysis Methods Partial differential equations Polynomials two grid algorithm virtual element method |
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| Title | Two-grid virtual element discretization of quasilinear elliptic problem |
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