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Title of Journal: Numer Math

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Abbravation: Numerische Mathematik

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Springer-Verlag

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DOI

10.1007/s12445-012-0168-6

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0945-3245

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Discrete minimum and maximum principles for finite

Authors: Ansgar Jüngel Andreas Unterreiter
Publish Date: 2004/11/26
Volume: 99, Issue: 3, Pages: 485-508
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Abstract

Uniform lower and upper bounds for positive finiteelement approximations to semilinear elliptic equations in several space dimensions subject to mixed DirichletNeumann boundary conditions are derived The main feature is that the nonlinearity may be nonmonotone and unbounded The discrete minimum principle provides a positivitypreserving approximation if the discretization parameter is small enough and if some structure conditions on the nonlinearity 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

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  1. Convergence rates for Tikhonov regularization of a two-coefficient identification problem in an elliptic boundary value problem
  2. A new class of symplectic integration schemes based on generating functions
  3. An optimal adaptive finite element method for elastoplasticity
  4. Galerkin and Runge–Kutta methods: unified formulation, a posteriori error estimates and nodal superconvergence
  5. Controllability of an Elliptic equation and its Finite Difference Approximation by the Shape of the Domain
  6. Decay rates of adaptive finite elements with Dörfler marking
  7. Multi-parameter regularization and its numerical realization
  8. Spectral conditions for admissibility and observability of wave systems: applications to finite element schemes
  9. Convergence of a semiclassical wavepacket based time-splitting for the Schrödinger equation
  10. A uniformly stable Fortin operator for the Taylor–Hood element
  11. A locking-free $$hp$$ DPG method for linear elasticity with symmetric stresses
  12. Pathwise approximation of stochastic differential equations on domains: higher order convergence rates without global Lipschitz coefficients
  13. The multi-level Monte Carlo finite element method for a stochastic Brinkman Problem
  14. Explicit trace inequalities for isogeometric analysis and parametric hexahedral finite elements
  15. Multi-level spectral galerkin method for the navier-stokes problem I : spatial discretization
  16. Hölder estimates for Green’s functions on convex polyhedral domains and their applications to finite element methods
  17. A residual–based error estimator for BEM–discretizations of contact problems
  18. An adaptive anisotropic perfectly matched layer method for 3-D time harmonic electromagnetic scattering problems
  19. Preconditioners for pseudodifferential equations on the sphere with radial basis functions
  20. Symmetric multistep methods for constrained Hamiltonian systems
  21. Numerical Eulerian method for linearized gas dynamics in the high frequency regime
  22. Proper generalized decomposition for nonlinear convex problems in tensor Banach spaces
  23. The boundary element spline collocation for nonuniform meshes on the torus
  24. Delay-dependent stability of high order Runge–Kutta methods
  25. Intrinsic finite element methods for the computation of fluxes for Poisson’s equation
  26. On generalized successive overrelaxation methods for augmented linear systems
  27. On the Lebesgue constant of barycentric rational interpolation at equidistant nodes
  28. A mixed finite element method for nonlinear elasticity: two-fold saddle point approach and a-posteriori error estimate
  29. Intrinsic representation of tangent vectors and vector transports on matrix manifolds
  30. Crouzeix–Raviart boundary elements
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