抄録
The finite cover method (FCM) is known as one of the generalized finite element methods and enjoys peculiar elements that partially have physical domains. We name them the generalized elements in this study and exmaine their performance within the framework of the finite element method (FEM). First, the elements with rectangular physical domain are studied by means of eigenvalues and eigenmodes of stiffness matrices. Secondly, the deformability of the elements with non-rectangular physical domain is also examined in comaprison with the corresponding FE solutions. Thirdly, assuming practical situations, in which sevral sizes of generalized elements are utilzed together, we report the cancellation errors in constructing global stiffness matrix when they have physical domans of significantly different order. Finally, after making the convergence study for the cook’s membrane problem and compiling all the results in this study, we conclude that the performance of generalized elements in the FCM are equivalent to or slightly superior to that of the FEM. It is to be noted that the studies also apply to the X-FEM and the GFEM.
