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Volume 13, Issue 4
Two-Grid Finite Volume Element Method Combined with Crank-Nicolson Scheme for Semilinear Parabolic Equations

Yuzhi Lou, Chuanjun Chen & Guanyu Xue

Adv. Appl. Math. Mech., 13 (2021), pp. 892-913.

Published online: 2021-04

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  • Abstract

The aim of the paper is to propose a second-order accurate Crank-Nicolson scheme for solving semilinear parabolic equations. This scheme combing two-grid finite volume element method involves solving a small nonlinear system on a coarse grid space and a linear system on a fine grid space, which can improve computing efficiency while keeping the accuracy. It means that we can use large time steps in the actual calculation. We further prove the optimal error estimates of the scheme strictly and present numerous simulations to demonstrate the theoretical results.

  • AMS Subject Headings

65N12, 65M60

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COPYRIGHT: © Global Science Press

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@Article{AAMM-13-892, author = {Lou , YuzhiChen , Chuanjun and Xue , Guanyu}, title = {Two-Grid Finite Volume Element Method Combined with Crank-Nicolson Scheme for Semilinear Parabolic Equations}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2021}, volume = {13}, number = {4}, pages = {892--913}, abstract = {

The aim of the paper is to propose a second-order accurate Crank-Nicolson scheme for solving semilinear parabolic equations. This scheme combing two-grid finite volume element method involves solving a small nonlinear system on a coarse grid space and a linear system on a fine grid space, which can improve computing efficiency while keeping the accuracy. It means that we can use large time steps in the actual calculation. We further prove the optimal error estimates of the scheme strictly and present numerous simulations to demonstrate the theoretical results.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.OA-2020-0064}, url = {http://global-sci.org/intro/article_detail/aamm/18756.html} }
TY - JOUR T1 - Two-Grid Finite Volume Element Method Combined with Crank-Nicolson Scheme for Semilinear Parabolic Equations AU - Lou , Yuzhi AU - Chen , Chuanjun AU - Xue , Guanyu JO - Advances in Applied Mathematics and Mechanics VL - 4 SP - 892 EP - 913 PY - 2021 DA - 2021/04 SN - 13 DO - http://doi.org/10.4208/aamm.OA-2020-0064 UR - https://global-sci.org/intro/article_detail/aamm/18756.html KW - Two-grid method, finite volume element method, Crank-Nicolson scheme, error estimates, semilinear parabolic equations. AB -

The aim of the paper is to propose a second-order accurate Crank-Nicolson scheme for solving semilinear parabolic equations. This scheme combing two-grid finite volume element method involves solving a small nonlinear system on a coarse grid space and a linear system on a fine grid space, which can improve computing efficiency while keeping the accuracy. It means that we can use large time steps in the actual calculation. We further prove the optimal error estimates of the scheme strictly and present numerous simulations to demonstrate the theoretical results.

Lou , YuzhiChen , Chuanjun and Xue , Guanyu. (2021). Two-Grid Finite Volume Element Method Combined with Crank-Nicolson Scheme for Semilinear Parabolic Equations. Advances in Applied Mathematics and Mechanics. 13 (4). 892-913. doi:10.4208/aamm.OA-2020-0064
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