In this paper, we study the simplest and the most standard adaptive finite element method for
the second-order nonmonotone quasi-linear elliptic problems with the exact solution u∈ H 0 …

In this paper, we establish the convergence and quasi-optimality of an adaptive finite
element method for nonmonotone elliptic problems on L 2 errors for a sufficiently fine initial …

A modified weak Galerkin finite element method is studied for nonmonotone quasilinear
elliptic problems. Using the contraction mapping theorem, the uniqueness of the solution to …

We investigate a stationary nonlinear heat conduction problem in which heat conductivities
depend on temperature. It is known that such problem need not have a unique solution even …

We introduce our main results on solving a nonlinear steady-state heat conduction problem
in anisotropic and nonhomogeneous media and its finite element approximation. In …

Abstract Comparison principles are developed for piecewise linear finite element
approximations of quasilinear elliptic partial differential equations. We consider the analysis …

We introduce our main results on solving a nonlinear steadystate heat conduction problem
in anisotropic and nonhomogeneous media and its finite element approximation. In …

We present a linear algebra approach to establishing a discrete comparison principle for a
nonmonotone class of quasilinear elliptic partial differential equations. In the absence of a …