Abstract
In this paper, a space-time spectral method is applied to approximate the linear multi-dimensional Sobolev equations. The Legendre-Galerkin method and a dual-Petrov-Galerkin discretization are employed in space and time, respectively. Being different from the general Legendre-Galerkin method, the technique adopted in this study lies in diagonalization of the mass matrix by using Fourier-like basis functions to save the computing time and memory. Moreover, the detailed stability analysis and error estimates are provided in the weighted space-time norms. We also formulate the matrix forms of the fully discrete scheme. Finally, extensive numerical tests are implemented to verify the theoretical results and demonstrate the efficiency of our method.
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