@Article{AAMM-10-1365, author = {Liu , D. J.Li , A. Q. and Chen , Z. R.}, title = {Nonconforming FEMs for the $p$-Laplace Problem}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2018}, volume = {10}, number = {6}, pages = {1365--1383}, abstract = {

The $p$-Laplace problems in topology optimization eventually lead to a degenerate convex minimization problem $E(v):= ∫_ΩW(∇v)dx − ∫_Ωf vdx$ for $v∈W^{1,p}_0(Ω)$ with unique minimizer $u$ and stress $σ := DW(∇u)$. This paper proposes the discrete Raviart-Thomas mixed finite element method (dRT-MFEM) and establishes its equivalence with the Crouzeix-Raviart nonconforming finite element method (CR-NCFEM). The sharper quasi-norm a priori and a posteriori error estimates of this two methods are presented. Numerical experiments are provided to verify the analysis.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.OA-2018-0117}, url = {http://global-sci.org/intro/article_detail/aamm/12715.html} }