Finite volume element methods for two-dimensional time fractional reaction–diffusion equations on triangular grids
Zhichao Fang, Jie Zhao, Hong Li, Yang Liu
Abstract
In this paper, time fractional reaction–diffusion equations with the Caputo fractional derivative are solved by using the classical L1-formula and the finite volume element (FVE) methods on triangular grids. The existence and uniqueness for the fully discrete FVE scheme are given. The stability results and optimal a priori error estimate in L2(Ω)-norm are derived, but it is difficult to obtain the corresponding results in H1(Ω)-norm, so another analysis technique is introduced and used to achieve our goal. Finally, some numerical results are given to verify the feasibility and effectiveness.
Topics & Concepts
MathematicsUniquenessReaction–diffusion systemNorm (philosophy)Fractional calculusFinite element methodA priori and a posterioriFinite volume methodApplied mathematicsStability (learning theory)GridMathematical analysisGeometryComputer scienceMechanicsEpistemologyPhysicsLawPhilosophyThermodynamicsMachine learningPolitical scienceFractional Differential Equations SolutionsDifferential Equations and Numerical MethodsNumerical methods for differential equations