Relaxation model for the p-Laplacian problem with stiffness

This paper proposes a new numerical scheme in 1-D for the p-Laplacian problem for the electromagnetic effects in a high-temperature Type II superconductors. The scheme is obtained by applying a relaxation approximation to the nonlinear derivatives in the problem. The new relaxation scheme achieves highly accurate results even for large p that makes the p-Laplacian flux stiff. The scheme is novel in that it is high-order accurate and predicts physically correct non-oscillatory magnetic fronts within these conductors, the later of which is not found by finite element approximate solutions done by the engineering community. The work is an extension of previous work on relaxation schemes applied to degenerate parabolic problems. Numerical tests are presented to validate the performance of the new scheme.