Efficient and Parallel Solution of High-Order Continuous Time Galerkin for Dissipative and Wave Propagation Problems

Abstract

SIAM Journal on Scientific Computing, Volume 46, Issue 3, Page A2073-A2100, June 2024.
Abstract. We propose efficient and parallel algorithms for the implementation of the high-order continuous time Galerkin method for dissipative and wave propagation problems. By using Legendre polynomials as shape functions, we obtain a special structure of the stiffness matrix that allows us to extend the diagonal Padé approximation to solve ordinary differential equations with source terms. The unconditional stability, [math] error estimates, and [math] superconvergence at the nodes of the continuous time Galerkin method are proved. Numerical examples confirm our theoretical results.