A posteriori error estimation for the dual mixed finite element method for the p-Laplacian in a polygonal domain

✍ Scribed by E. Creuse; M. Farhloul; L. Paquet

• Publisher: Elsevier Science
• Year: 2007
• Tongue: English
• Weight: 382 KB
• Volume: 196
• Category: Article
• ISSN: 0045-7825
• DOI: 10.1016/j.cma.2006.11.023

✦ Synopsis

For the discrete solution of the dual mixed formulation for the p-Laplace equation, we define two residues R and r. Then we bound the norm of the errors on the two unknowns in terms of the norms of these two residues. Afterwards, we bound the norms of these two residues by functions of two error estimators whose expressions involve at the very most the datum and the computed quantities. We next explain how the discretized dual mixed formulation is hybridized and solved. We close our paper by numerical tests for p ¼ 1:8 and p ¼ 3 firstly to corroborate the orders of convergence established by Farhloul and Manouzi [M. Farhloul, H. Manouzi, On a mixed finite element method for the p-Laplacian, Canadian Applied Mathematics Quarterly 8 (2000) 67-78], and secondly to experimentally verify the reliability of our a posteriori error estimates.