A variationally separable splitting for the generalized‐α method for parabolic equations

We present a variationally separable splitting technique for the generalized‐α method for solving parabolic partial differential equations. We develop a technique for a tensor‐product mesh which results in a solver with a linear cost with respect to the total number of degrees of freedom in the system for multidimensional problems. We consider finite elements and isogeometric analysis for the spatial discretization. The overall method maintains user‐controlled high‐frequency dissipation while minimizing unwanted low‐frequency dissipation. The method has second‐order accuracy in time and optimal rates (hp+1 in L2 norm of u and hp in L2 norm of ∇u) in space. We present the spectral analysis on the amplification matrix to establish that the method is unconditionally stable. Various numerical examples illustrate the performance of the overall methodology and show the optimal approximation accuracy.