SUPERCONVERGENCE ANALYSIS FOR TIME-FRACTIONAL DIFFUSION EQUATIONS WITH NONCONFORMING MIXED FINITE ELEMENT METHOD

doi:10.4208/jcm.1805-m2017-0256

In this paper, a fully discrete scheme based on the L1 approximation in temporal direction for the fractional derivative of order in (0, 1) and nonconforming mixed finite element method (MFEM) in spatial direction is established. First, we prove a novel result of the consistency error estimate with order O(h²) of EQ₁^rot element (see Lemma 2.3). Then, by using the proved character of EQ₁^rot element, we present the superconvergent estimates for the original variable u in the broken H¹-norm and the flux p=∇u in the (L²)²-norm under a weaker regularity of the exact solution. Finally, numerical results are provided to confirm the theoretical analysis.

Key words: Nonconforming MFEM, L1 method, Time-fractional diffusion equations, Superconvergence

CLC Number:

65N15
65N30

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Abstract

SUPERCONVERGENCE ANALYSIS FOR TIME-FRACTIONAL DIFFUSION EQUATIONS WITH NONCONFORMING MIXED FINITE ELEMENT METHOD

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