Numerical manifold method for the potential problem

Usually,the governing equations of the numerical manifold method(NMM) are derived from the minimum potential energy principle.For many practical problems,it is very difficult to derive the governing equations of the numerical manifold method with the variational principle.So we should implement the method of weighted residuals to derive the governing equations of the NMM.The numerical manifold method of Laplace equation was presented,it was also more general than the minimum potential energy principle to obtain the governing equations of the NMM.At the same time,the method enriched the mathematical foundation of NMM and extended fields of application.At last,the validity of the method was illustrated by use of two numerical examples.