@article{4148dfb6969f4d80a8f68a450f76e5c3, title = "Higher order FEM for the obstacle problem of the p-Laplacian: A variational inequality approach", abstract = "We consider higher order finite element discretizations of a nonlinear variational inequality formulation arising from an obstacle problem with the p-Laplacian differential operator for pā(1,ā). We prove an a priori error estimate and convergence rates with respect to the mesh size h and in the polynomial degree q under assumed regularity. Moreover, we derive a general a posteriori error estimate which is valid for any uniformly bounded sequence of finite element functions. All our results contain the known results for the linear case of p=2. We present numerical results on the improved convergence rates of adaptive schemes (mesh size adaptivity with and without polynomial degree adaptation) for the singular case of p=1.5 and for the degenerated case of p=3.", keywords = "A posteriori error estimate, A priori error estimate, hq-adaptive FEM, p-Laplacian obstacle problem", author = "Lothar Banz and Lamichhane, {Bishnu P.} and Stephan, {Ernst P.}", note = "Funding information: The visit of the third author to the University of Newcastle, Australia was partially supported by the priority research centre of the University of Newcastle for Computer-Assisted Research Mathematics and its Applications . He expresses his sincere thanks to Bishnu Lamichhane for his hospitality during the visit.", year = "2018", month = oct, day = "1", doi = "10.1016/j.camwa.2018.07.016", language = "English", volume = "76", pages = "1639--1660", journal = "Computers and Mathematics with Applications", issn = "0898-1221", publisher = "Elsevier Ltd.", number = "7", }