| Summary: | In this article, the time-fractional reaction-diffusion equations are solved by using a mixed finite volume element (MFVE) method and the <inline-formula> <math display="inline"> <semantics> <mrow> <mi>L</mi> <mn>1</mn> </mrow> </semantics> </math> </inline-formula>-formula of approximating the Caputo fractional derivative. The existence, uniqueness and unconditional stability analysis for the fully discrete MFVE scheme are given. <i>A priori</i> error estimates for the scalar unknown variable (in <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) and the vector-valued auxiliary variable (in <inline-formula> <math display="inline"> <semantics> <msup> <mrow> <mo>(</mo> <msup> <mi>L</mi> <mn>2</mn> </msup> <mrow> <mo>(</mo> <mo>Ω</mo> <mo>)</mo> </mrow> <mo>)</mo> </mrow> <mn>2</mn> </msup> </semantics> </math> </inline-formula>-norm and <inline-formula> <math display="inline"> <semantics> <mrow> <mi mathvariant="bold-italic">H</mi> <mo>(</mo> <mi>div</mi> <mo>,</mo> <mo>Ω</mo> <mo>)</mo> </mrow> </semantics> </math> </inline-formula>-norm) are derived. Finally, two numerical examples in one-dimensional and two-dimensional spatial regions are given to examine the feasibility and effectiveness.
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