Accuracy versus cost for three efficient finite-element solvers

Three efficient finite-element schemes are compared for Poisson problems on triangular meshes: (1) uniform subdivision of first order triangles and the incomplete Choleski conjugate gradient method; (2) uniform subdivision of first-order triangles and a multilevel preconditioned conjugate gradient method; and (3) uniform increase of polynomial order and diagonally-preconditioned conjugate gradients. Errors in the computed energy, and computational costs, are obtained for a square, air-filled coaxial cable; a linear, current-driven magnetostatic problem; and a microstrip transmission line. Increasing the polynomial order is by far the best approach, i.e. gives the best accuracy for a given cost