  We consider 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 lower order term, we require local conditions on
the mesh to establish the comparison principle and uniqueness of the piecewise
linear finite element solution. We consider the assembled matrix corresponding
to the linearized problem satisfied by the difference of two solutions to the
nonlinear problem. Monotonicity of the assembled matrix establishes a maximum
principle for the linear problem and a comparison principle for the nonlinear
problem. The matrix analysis approach to the discrete comparison principle
yields sharper constants and more relaxed mesh conditions than does the
argument by contradiction used in previous work.
