FUNDAMENTAL PERFORMANCE IN THREE-DIMENSIONAL SEEPAGE PROBLEMS OF FINITE ELEMENTS USING THE RAVIART-THOMAS MIXED INTERPOLATION

Abstract

 This paper reports the results of a series of numerical experiments concerning the fundamental performance in solving three-dimensional (3D) seepage problems of finite elements using the Raviart-Thomas mixed interpolation method (RT), which is capable of independent interpolation of hydraulic head and velocity. In the conventional finite element method that uses only hydraulic head as an unknown variable, velocity is independently calculated for each element. There are cases, therefore, where a continuous velocity field cannot be determined with high accuracy. In the RT method, flux can be made continuous along common boundaries of adjacent elements because a velocity shape function is constructed by using the set of flux defined at the element faces as a degree of freedom. Furthermore, by means of formulation based on a hybrid variational principle, final variables can be reduced to the Lagrange multiplier. Although almost all of the previous studies have shown validity in solving two-dimensional problems, this study identifies the fundamental performance, including drawbacks, of 3D elements used in the RT method in solving seepage problems.