Bulletin of the Korean Mathematical Society (대한수학회보)
- Volume 35 Issue 2
- /
- Pages.345-362
- /
- 1998
- /
- 1015-8634(pISSN)
- /
- 2234-3016(eISSN)
ERROR ESTIMATIES FOR A FREQUENCY-DOMAIN FINITE ELEMENT METHOD FOR PARABOLIC PROBLEMS WITH A NEUMANN BOUNDARY CONDITION
Abstract
We introduce and anlyze a naturally parallelizable frequency-domain method for parabolic problems with a Neumann boundary condition. After taking the Fourier transformation of given equations in the space-time domain into the space-frequency domain, we solve an indefinite, complex elliptic problem for each frequency. Fourier inversion will then recover the solution of the original problem in the space-time domain. Existence and uniqueness of a solution of the transformed problem corresponding to each frequency is established. Fourier invertibility of the solution in the frequency-domain is also examined. Error estimates for a finite element approximation to solutions fo transformed problems and full error estimates for solving the given problem using a discrete Fourier inverse transform are given.
Keywords
- parabolic problems;
- Neumann boundary conditions;
- frequency-domain methods;
- finite element methods;
- parallel algorithm;
- Fourier transform