Quadratic Finite Volume Element Methods Based on Optimal Stress Points for Solving One-Dimensional Parabolic Problems

摘要

A new Lagrangian quadratic finite volume element method based on optimal stress points was presented for solving one-dimensional parabolic problem with trial and test spaces as the Lagrangian quadratic finite volume element space and the piecewise constant function space respectively. It is proved that the method has optimal order H~1 and L~2 error estimates. The numerical experiment confirms the results of theoretical analysis.