On theories and applications of mixed finite element methods for linear boundary-value problems

AbstractThis paper is devoted to a study of mathematical properties of certain mixed finite element approximations of linear boundary-value problems, and the application of such methods to simple representative problems which are designed to test the validity of the theory. In particular, the Oden—Reddy theory[1,2] is studied in some depth. An alternate approach to convergence questions, suggested by certain theorems of Babuška[3], is also devised, and predictions of the two theories are briefly compared. As a result of this investigation, a number of criteria for using mixed methods in practical problems are identified, and it is shown that these criteria are supported by both theoretical arguments and by numerical experiments