- 3.10. One dimensional advection of square wave on domain Ω = [0, 10] subdivided into 10 equally-sized elements. . . . . . . . . . . . . . . . . . . . .
- 3.11. Comparison of Galerkin projection for the Gaussian function of ((a), (b)) spectral/hp element method and ((c), (d)) linear finite element method for DOF = 90 and the corresponding L2 and L∞ error for increasing DOF ((e), (f)). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
- 3.12. Comparison of Galerkin projection for the hat function of ((a), (b)) spectral/hp element method and ((c), (d)) linear finite element method for DOF = 90 and the corresponding L2 and L∞ error for increasing DOF ((e), (f)). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
- 3.13. Comparison of Galerkin projection for the square wave function of ((a), (b)) spectral/hp element method and ((c), (d)) linear finite element method for DOF = 90 and the corresponding L2 and L∞ error for increasing DOF ((e), (f)). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
- 3.14. Comparison of the numerical results for the advection equation after 30000 timesteps with Δt = 10−4 using the continuous Galerkin method and the discontinuous Galerkin method for the spectral/hp element method for P = 8, Nel = 10 ((a), (b)) and the linear finite element method, i.e. P = 1, for Nel = 45 ((c), (d)) for the smooth Gaussian function and the L2 and L∞ error for increasing DOF ((e), (f)). . . . . . . . . . . . . . .
- 3.15. Comparison of the numerical results for the advection equation after 30000 timesteps with Δt = 10−4 using the continuous Galerkin method and the discontinuous Galerkin method for the spectral/hp element method for P = 8, Nel = 10 ((a), (b)) and the linear finite element method, i.e. P = 1, for Nel = 45 ((c), (d)) for the hat function and the L2 and L∞ error for increasing DOF ((e), (f)). . . . . . . . . . . . . . . . . . . . . .
- 3.16. Comparison of the numerical results for the advection equation after 30000 timesteps with Δt = 10−4 using the continuous Galerkin method and the discontinuous Galerkin method for the spectral/hp element method for P = 8, Nel = 10 ((a), (b)) and the linear finite element method, i.e. P = 1, for Nel = 45 ((c), (d)) for the hat function and the L2 and L∞ error for increasing DOF ((e), (f)). . . . . . . . . . . . . . . . . . . . . .
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