| Summary: | In this paper, a finite volume element (FVE) method is proposed for the time fractional Sobolev equations with the Caputo time fractional derivative. Based on the <inline-formula><math display="inline"><semantics><mrow><mi>L</mi><mn>1</mn></mrow></semantics></math></inline-formula>-formula and the Crank–Nicolson scheme, a fully discrete Crank–Nicolson FVE scheme is established by using an interpolation operator <inline-formula><math display="inline"><semantics><msubsup><mi>I</mi><mi>h</mi><mo>*</mo></msubsup></semantics></math></inline-formula>. The unconditional stability result and the optimal a priori error estimate in the <inline-formula><math display="inline"><semantics><mrow><msup><mi>L</mi><mn>2</mn></msup><mrow><mo>(</mo><mo>Ω</mo><mo>)</mo></mrow></mrow></semantics></math></inline-formula>-norm for the Crank–Nicolson FVE scheme are obtained by using the direct recursive method. Finally, some numerical results are given to verify the time and space convergence accuracy, and to examine the feasibility and effectiveness for the proposed scheme.
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