Finite element method for two-dimensional time-fractional Tricomi-type equations (Q2846174)

The authors study the finite element method (FEM) for two-dimensional time-fractional Tricomi-type equations, which for special values of the parameters involved reduce to the linear Tricomi equation. The FEM has been used to find the variational solution to space fractional partial differential equations (see, for example [\textit{V. J. Ervin, N. Heuer} and \textit{J. P. Roop}, SIAM J. Numer. Anal. 45, No. 2, 572--591 (2007; Zbl 1141.65089)]), where the temporal derivative is the classical derivative and the spatial derivative is of fractional order. The stability analysis and error estimates for the full discrete scheme are discussed. The convergence rate of the method is proved to be optimal. Numerical tests are given to demonstrate that the superconvergence can be observed in many more cases.