A two-grid method for finite element solutions of nonlinear parabolic equations (Q696065)

Summary: A two-grid method is presented and discussed for a finite element approximation to a nonlinear parabolic equation in two space dimensions. Piecewise linear trial functions are used. In this two-grid scheme, the full nonlinear problem is solved only on a coarse grid with grid size \(H\). The nonlinearities are expanded about the coarse grid solution on a fine gird of size \(h\), and the resulting linear system is solved on the fine grid. A priori error estimates are derived with the \(H^1\)-norm \(O(h + H^2)\) which shows that the two-grid method achieves asymptotically optimal approximation as long as the mesh sizes satisfy \(h = O(H^2)\). An example is also given to illustrate the theoretical results.