An Expanded Mixed Finite Element Method for Fractional Dispersion Equations with Variable Coefficient

In this article, we propose an expanded mixed finite element method for variable-coefficient fractional dispersion equations (FDEs). By introducing two intermediate variables, p=Du and σ=−Iθβp, the FDEs are reformulated into a mixed system involving only lower-order derivatives. Based on this, we construct an expanded mixed variational framework and prove the weak coercivity in the sense of the LBB condition over appropriately chosen Sobolev spaces, thereby ensuring the well-posedness of the formulation. Then, we develop an expanded mixed finite element scheme and prove that the unique expanded finite element solution possesses optimal approximation accuracy to the fractional flux σ, the gradient p and the unknown u. Finally, numerical experiments are conducted to verify the efficiency and accuracy of the proposed method.