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 - <p style="text-align: justify;">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.</p>