ON SOLVING ELLIPTIC EQUATIONS TO MODERATE ACCURACY

We compare the computer costs for several finite element methods for linear, self -adjoint, elliptic boundary-value problems on two-dimensional rectangular domains. We consider the efficiency of the assembly phase in each method, and in some cases point out improvements to previous work. Moreover, we develop approximate operation counts for the solve phase which indicate that it is advantageous to use basis functions which are as smooth as possible.We present the results of testing fourth-order versions of the methods on some of the problems from Houstis and Rice (CSD-TR 263, Computer Science Department, Purdue University, West Lafayette IN 1978). Our results contrast with those of the study of Houstis et al. (J. Comp. Phys. 27 (1978), pp. 323–350). First, the Rayleigh–Ritz–Galerkin method with bicubic Hermites is almost always as efficient as the collocation method; the contrast appears to be due to more efficient assembly phase techniques. Second, we present an example of a problem for which evaluating ...