The numerical solution of the homogeneous Dirichlet problem for the p-Laplacian is considered. We propose an adaptive algorithm with continuous piecewise affine finite elements and prove that the approximate solutions converge to the exact one. While the algorithm is a rather straight-forward generalization of those for the linear case p=2, the proof of its convergence is different. In particular, it does not rely on a strict error reduction.
Convergent adaptive finite elements for the nonlinear Laplacian / A. Veeser. - In: NUMERISCHE MATHEMATIK. - ISSN 0029-599X. - 92:4(2002), pp. 743-770.
Convergent adaptive finite elements for the nonlinear Laplacian
A. VeeserPrimo
2002
Abstract
The numerical solution of the homogeneous Dirichlet problem for the p-Laplacian is considered. We propose an adaptive algorithm with continuous piecewise affine finite elements and prove that the approximate solutions converge to the exact one. While the algorithm is a rather straight-forward generalization of those for the linear case p=2, the proof of its convergence is different. In particular, it does not rely on a strict error reduction.File in questo prodotto:
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