Time discretizations of both the heat equation and the advection-diffusion equation in two space variables are analyzed. For space approximation the pseudospectral Chebyshev method, which enjoys infinite order of accuracy for smooth solutions, is used. The equation is collocated at the Gauss-Chebyshev points, and derivatives are computed by the pseudospectral differencing technique. At any time interval the pseudospectral solution, which is a polynomial of degree N, is advanced in time using the implicit theta -method for the diffusive part of the equation, while the advective terms is dealt with explicitly. We prove unconditional stability and optimal error bounds, depending on both N and DELTA t (the time-step), in the norms of the weighted Sobolev spaces.
ANALYSIS OF CHEBYSHEV COLLOCATION METHODS FOR PARABOLIC EQUATIONS
QUARTERONI, ALFIO MARIA
1986-01-01
Abstract
Time discretizations of both the heat equation and the advection-diffusion equation in two space variables are analyzed. For space approximation the pseudospectral Chebyshev method, which enjoys infinite order of accuracy for smooth solutions, is used. The equation is collocated at the Gauss-Chebyshev points, and derivatives are computed by the pseudospectral differencing technique. At any time interval the pseudospectral solution, which is a polynomial of degree N, is advanced in time using the implicit theta -method for the diffusive part of the equation, while the advective terms is dealt with explicitly. We prove unconditional stability and optimal error bounds, depending on both N and DELTA t (the time-step), in the norms of the weighted Sobolev spaces.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
