A full discrete two-grid finite-volume method for a nonlinear parabolic problem

Abstract

A fully discrete two-grid finite-volume method (FVM) for a nonlinear parabolic problem is studied in this paper. This method involves solving a nonlinear parabolic equation on coarse mesh space and a linearized parabolic equation on fine grid. Both L ² and H ¹ norm error estimates of the standard FVM for the nonlinear parabolic problem are derived. Compared with the standard FVM, the two-level method is of the same order as the one-level method in the H ¹-norm as long as the mesh sizes satisfy h=𝒪(H ^3/2). However, the two-level method involves much less work than the standard method. Numerical results are provided to demonstrate the effectiveness of our algorithm.

Keywords:

• two-grid
• finite-volume method
• nonlinear parabolic problem
• error estimate

2000 Mathematics Subject Classifications :

• 65N12
• 74S10

Additional information

Notes on contributors

Tong Zhang

Present address: School of Mathematics & Information Science, Henan Polytechnic University, Jiaozuo 454003, China.