@Article{IJNAM-12-197, author = {}, 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} }