In this paper an abstract error estimate theorem is given for finite element approximation of selfadjoint compact operators eigenvalue problems, and several new results are obtained by applying the theorem to conforming finite element method for second order elliptic problems, and mixed finite element method for the biharmonic problem.
In this paper, the Relaxed-ILU preconditioner is applied to solve the linear equations arising from the black oil models. Numerical experiments demonstrate that the method is superior to the ILU preconditioner which is already extensively used in reservoir simulations. We have implemented the relaxed-ILU preconditioner into some practical reservoir simulators.
In this paper, a non-matching non-overlapping domain decomposition method for solving 3-dimensional problems is presented. Based on the method, we developed a powerful software which is suitable for solving practical problems. An application to numerical reservoir simulation is given to demonstrate the method.
