Tj. Janik et S. Jensen, ON THE STABILITY AND PERFORMANCE OF THE P-VERSION OF THE FINITE-ELEMENT METHOD FOR 1ST-ORDER HYPERBOLIC PROBLEMS, Applied numerical mathematics, 15(4), 1994, pp. 407-437
We study the p-version of the finite element method for the first-orde
r scalar hyperbolic equation with constant coefficients. We analyze th
e stability and convergence of the method. A comparison with the disco
ntinuous h-version and results of numerical experiments are also prese
nted.