1997 Volume 40 Issue 1 Pages 121-125
The stability of time-stepping methods for parabolic differential equations is critical issue. Furthermore, solving such equations with a classical time-stepping approach can be very expensive because many small time steps have to be taken if steep gradients occur in the solution, even if they occur only in a small part of the space domain. In this paper we present a discretization technique in which finite element approximations are used in time and space simultaneously for a relatively large time period called a time slab. The weighted residual process is used to formulate a finite element method for a space-time domain based upon the continuous Galerkin method. This technique may be repeatedly applied to obtain further parts of the solution in subsequent time intervals.
JSME international journal. Ser. 1, Solid mechanics, strength of materials
JSME international journal. Ser. A, Mechanics and material engineering
JSME international journal. Ser. 3, Vibration, control engineering, engineering for industry
JSME international journal. Ser. C, Dynamics, control, robotics, design and manufacturing
JSME International Journal Series A Solid Mechanics and Material Engineering