We introduce and analyze a robust nonconforming finite element method for a three-dimensional singularly perturbed quad-curl model problem.For the solution of the model problem,we derive proper a priori bounds,based on which we prove that the proposed finite element method is robust with respect to the singular perturbation parameter e and the numerical solution is uniformly convergent with order h1/2.In addition,we investigate the effect of treating the second boundary condition weakly by Nitsche's method.We show that such a treatment leads to sharper error estimates than imposing the boundary condition strongly when the parameterε＜h.Finally,numerical experiments are provided to illustrate the good performance of the method and confirm our theoretical predictions.
维普
万方数据