Abstract:

Based on the Lagrangian cubic element finite volume method for Poisson equation on triangular meshes constructed by us, we found that the convergence rate of average gradient of the numerical solutions is approximately 4 order at the symmetrical points of triangular element (i.e.midpoints of three edges and three vertices) through the numerical experiments,  which is nearly one order higher than that of the H¹ norm (O(h³)).

Key words: finite volume element method, Lagrange cubic basis, dual partition, superconvergence