A Non-uniform H2N2 Galerkin FEM for the Time Fractional Diffusion-Wave Equation

In this paper, we first construct an H2N2 approximation on the time nonuniform meshes, i.e., graded meshes for the Caputo derivative of order in \((1,2)\) and present a global convergence analysis under the reasonable regularity assumptions. The temporal nonuniform H2N2 formula is then combined with the Galerkin finite element method (FEM) to develop an H2N2-FEM scheme for the time fractional diffusion-wave equation. By virtue of discrete complementary convolution (DCC) kernels, stability, convergence, and error estimate of the proposed H2N2-FEM scheme are proved. Numerical results are presented to support our theoretical analysis.