A High‐Order Finite Element Method for Solving Two‐Dimensional Fractional Rayleigh–Stokes Problem for a Heated Generalized Second Grade Fluid

ABSTRACT This article develops a high‐order finite element scheme in an approximate solution of the two‐dimensional Rayleigh–Stokes problem for a heated generalized second‐grade fluid with fractional derivatives. The constructed approach consists of approximating the exact solution by interpolation in time while the finite element technique is used in the approximation of the spatial derivatives. This combination is simple and easy to implement. The stability and error estimates of the developed strategy are deeply analyzed in the ‐norm. The theoretical studies suggest that the proposed method is unconditionally stable, convergent with order , faster, and more efficient than a broad range of numerical schemes discussed in the literature for the considered time fractional partial differential equation. Some numerical examples are carried out to show the applicability and viability of the new algorithm.