Discrete minimum and maximum principles for finite element approximations of non-monotone elliptic equations

Abstract

Uniform lower and upper bounds for positive finite-element approximations to semilinear elliptic equations in several space dimensions subject to mixed Dirichlet-Neumann boundary conditions are derived. The main feature is that the non-linearity may be non-monotone and unbounded. The discrete minimum principle provides a positivity-preserving approximation… (More)
DOI: 10.1007/s00211-004-0554-5

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Cite this paper

@article{Jngel2005DiscreteMA, title={Discrete minimum and maximum principles for finite element approximations of non-monotone elliptic equations}, author={Ansgar J{\"{u}ngel and Andreas Unterreiter}, journal={Numerische Mathematik}, year={2005}, volume={99}, pages={485-508} }