In this article,a weak Galerkin finite element method for the Laplace equation using the harmonic polynomial space is proposed and analyzed.The idea of using the Pk-harmonic polynomial space instead of the full polynomial space Pk is to use a much smaller number of basis functions to achieve the same accuracy when k≥2.The optimal rate of convergence is derived in both H1 and L2 norms.Numerical experiments have been conducted to verify the theoretical error estimates.In addition,numerical comparisons of using the P2-harmonic polynomial space and using the standard P2 polynomial space are presented.
展开▼
