In this paper, we examine some computational issues on finite element discretization of the p-Laplacian. We introduced a class of descent methods with multi-grid finite element preconditioners, and carried out convergence analysis. We showed that their convergence rate is mesh-independent. We studied the behavior of the algorithms with large p. Our numerical tests show that these algorithms are able to solve large scale p-Laplacian with very large p. The algorithms are then used to solve a variational inequality.
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Huang, Y.Q., Li, R. & Liu, W. Preconditioned Descent Algorithms for p-Laplacian. J Sci Comput 32, 343–371 (2007). https://doi.org/10.1007/s10915-007-9134-z
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DOI: https://doi.org/10.1007/s10915-007-9134-z
Keywords
- Highly degenerate p-Laplacian
- finite element approximation
- preconditioned steepest descent algorithms
- variational inequalities