Optimal error analysis of a non-uniform IMEX-L1 finite element method for time fractional PDEs and PIDEs
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Stability and optimal convergence analysis of a non-uniform implicit-explicit L1 finite element method (IMEX-L1-FEM) are studied for a class of time-fractional linear partial differential/integro-differential equations with non-self-adjoint elliptic part having variable (space-time) coefficients. Non-uniform IMEX-L1-FEM is based on a combination of an IMEX-L1 method on graded mesh in the temporal direction and a finite element method in the spatial direction. A discrete fractional Grönwall inequality is proposed, which enables us to derive optimal error estimates in L^2- and H^1-norms. Numerical experiments are presented to validate our theoretical findings.
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