Abstract:

A new  Lagrangian quadratic finite volume element method based on optimal stress points was presented for solving
onedimensional parabolic problems with trial and test spaces as the Lagrangian quadratic finite element space and the piecewise constant function space respectively. It is proved that the method has optimal order H¹ and L² error estimates. In addition, we discussed the global superconvergence in H¹ norm and the locally pointwise superconvergence of numerical derivatives at optimal stress points. The numerical experiment confirms the results of theoretical analysis.

Key words: quadratic finite volume element methods, parabolic equations, optimal stress points, error estimate