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

Autor: Ansgar Jüngel, Andreas Unterreiter
Rok vydání: 2004
Předmět:
Zdroj: Numerische Mathematik. 99:485-508
ISSN: 0945-3245
0029-599X
DOI: 10.1007/s00211-004-0554-5
Popis: 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 if the discretization parameter is small enough and if some structure conditions on the non-linearity and the triangulation are assumed. The discrete maximum principle also holds for degenerate diffusion coefficients. The proofs are based on Stampacchia’s truncation technique and on a variational formulation. Both methods are settled on careful estimates on the truncation operator.
Databáze: OpenAIRE
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