P-Continuous Method For P-Laplacian

In this paper we mainly study the numerical methods for the large scale p—Laplacian problems. Based on the Steepest Descent Algorithm with Weighted Preconditioner numerical method, we introduce the p-continuous ideas, proposed the p-continuous Steepest Descent Algorithm with Weighted Preconditioner (PSD algorithm), Hybrid Conjugate Gradient based on Steepest Descent Algorithm with Weighted Preconditioner (SDCG algorithm) and p-continuous Hybrid Conjugate Gradient based on Steepest Descent Algorithm with Weighted Preconditioner (PSDCG algorithm), and partly proved their convergence. Also, we proposed completely multi-grid algorithm by combining these algorithms with multi-grid iterated techniques. Finally, we gave some numerical examples, the numerical results show that, comparison with the old algorithms, our new algorithms are more stable, efficiency, and work well for the large scope of p value.