Abstract：There exist many weak discontinuity problems such as inclusion problems in the practical engineering computations. For the commonly used finite element (FEM) methods, mesh refinement or the increase of element order throughout the domain is usually used in order to ensure that each point on the interface can satisfy the given high degree of accuracy. But this will lead to rapid growth of the computer’s physical memory and the CPU time. The p-version adaptive FEM method is an efficient numerical method which can greatly improve the accuracy of calculation through adaptively increasing the order of elements used in the FEM analysis. In this paper, we have designed the corresponding p-version adaptive FEM method for modeling the weak discontinuity problems and emphatically discussed the influence of different error control standards on the computational results of each point on the interface. Moreover, we have made the numerical computation and simulation for some typical weak discontinuity problems. The numerical results are shown that the p-version adaptive FEM method is very efficient for the solution of the weak discontinuity problems, and the efficiency can be greatly improved by obtaining the reliable numerical results with fewer elements.
2016, Vol. 37 
