title: Numerical analysis of an H1-Galerkin mixed finite element method for time fractional telegraph equation.
abstract: We discuss and analyze an H(1)-Galerkin mixed finite element (H(1)-GMFE) method to look for the numerical solution of time fractional telegraph equation. We introduce an auxiliary variable to reduce the original equation into lower-order coupled equations and then formulate an H(1)-GMFE scheme with two important variables. We discretize the Caputo time fractional derivatives using the finite difference methods and approximate the spatial direction by applying the H(1)-GMFE method. Based on the discussion on the theoretical error analysis in L(2)-norm for the scalar unknown and its gradient in one dimensional case, we obtain the optimal order of convergence in space-time direction. Further, we also derive the optimal error results for the scalar unknown in H(1)-norm. Moreover, we derive and analyze the stability of H(1)-GMFE scheme and give the results of a priori error estimates in two- or three-dimensional cases. In order to verify our theoretical analysis, we give some results of numerical calculation by using the Matlab procedure.
authors.affiliation: School of Statistics and Mathematics, Inner Mongolia University of Finance and Economics, Hohhot 010070, China.
authors.forename: Jinfeng
authors.initials: J
authors.lastname: Wang
authors.affiliation: School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, China.
authors.forename: Meng
authors.initials: M
authors.lastname: Zhao
authors.affiliation: School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, China.
authors.forename: Min
authors.initials: M
authors.lastname: Zhang
authors.affiliation: School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, China.
authors.forename: Yang
authors.initials: Y
authors.lastname: Liu
authors.affiliation: School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, China.
authors.forename: Hong
authors.initials: H
authors.lastname: Li
mesh_terms: D000465:Algorithms; D008962:Models, Theoretical