부산대학교 도서관

This paper analyzes the accuracy of solving wave, hyperbolic andSchrödinger equations by the spectral element method. Firstly, theauthors demonstrate that the spectral scheme constructed by the $Q^k$continuous finite element method with $k+1$-point Gauss-Lobattoquadrature on rectangular meshes for solving wave equations is$k+2$-order accurate in the discrete 2-norm for smooth solutions. Thesame proof can be extended to the spectral element method for solvinglinear parabolic and Schrödinger equations. Moreover, the main resultalso applies to the spectral element method on curvilinear meshes thatcan be smoothly mapped to rectangular meshes on the unit square.\par Compared with other numerical methods, the high accuracy of thespectral element method has obvious advantages. However, thealgorithmic principle of the spectral element method restricts thecomputational efficiency to some extent. The study of the errorestimation for linear PDEs is meaningful; especially if it can beextended to nonlinear equations.