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Volume 12, Issue 2
A Two-Grid Finite Volume Element Method for a Nonlinear Parabolic Problem

Chuanjun Chen & Wei Liu

Int. J. Numer. Anal. Mod., 12 (2015), pp. 197-210.

Published online: 2015-12

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  • Abstract

A two-grid algorithm is presented and discussed for a finite volume element method to a nonlinear parabolic equation in a convex polygonal domain. The two-grid algorithm consists of solving a small nonlinear system on a coarse-grid space with grid size $H$ and then solving a resulting linear system on a fine-grid space with grid size $h$. Error estimates are derived with the $H^1$-norm $O(h+H^2)$ which shows that the two-grid algorithm achieves asymptotically optimal approximation as long as the mesh sizes satisfy $h=O(H^2)$. Numerical examples are presented to validate the usefulness and efficiency of the method.

  • Keywords

Two-grid, finite volume element method, nonlinear parabolic equation, error estimates.

  • AMS Subject Headings

65M12, 65M15, 65M60

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-12-197, author = {Chuanjun Chen and Wei Liu}, title = {A Two-Grid Finite Volume Element Method for a Nonlinear Parabolic Problem}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2015}, volume = {12}, number = {2}, pages = {197--210}, abstract = {

A two-grid algorithm is presented and discussed for a finite volume element method to a nonlinear parabolic equation in a convex polygonal domain. The two-grid algorithm consists of solving a small nonlinear system on a coarse-grid space with grid size $H$ and then solving a resulting linear system on a fine-grid space with grid size $h$. Error estimates are derived with the $H^1$-norm $O(h+H^2)$ which shows that the two-grid algorithm achieves asymptotically optimal approximation as long as the mesh sizes satisfy $h=O(H^2)$. Numerical examples are presented to validate the usefulness and efficiency of the method.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/484.html} }
TY - JOUR T1 - A Two-Grid Finite Volume Element Method for a Nonlinear Parabolic Problem AU - Chuanjun Chen & Wei Liu JO - International Journal of Numerical Analysis and Modeling VL - 2 SP - 197 EP - 210 PY - 2015 DA - 2015/12 SN - 12 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/484.html KW - Two-grid, finite volume element method, nonlinear parabolic equation, error estimates. AB -

A two-grid algorithm is presented and discussed for a finite volume element method to a nonlinear parabolic equation in a convex polygonal domain. The two-grid algorithm consists of solving a small nonlinear system on a coarse-grid space with grid size $H$ and then solving a resulting linear system on a fine-grid space with grid size $h$. Error estimates are derived with the $H^1$-norm $O(h+H^2)$ which shows that the two-grid algorithm achieves asymptotically optimal approximation as long as the mesh sizes satisfy $h=O(H^2)$. Numerical examples are presented to validate the usefulness and efficiency of the method.

Chuanjun Chen and Wei Liu. (2015). A Two-Grid Finite Volume Element Method for a Nonlinear Parabolic Problem. International Journal of Numerical Analysis and Modeling. 12 (2). 197-210. doi:
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