Discrete maximum principle for linear parabolic problems solved on hybrid meshes
Applied Numerical Mathematics - Tenth seminar on and differential-algebraic equations (NUMDIFF-10)
On the design of general-purpose flux limiters for finite element schemes. I. Scalar convection
Journal of Computational Physics
On discrete maximum principles for nonlinear elliptic problems
Mathematics and Computers in Simulation
Journal of Computational Physics
A monotone finite volume method for advection-diffusion equations on unstructured polygonal meshes
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Linearity-preserving flux correction and convergence acceleration for constrained Galerkin schemes
Journal of Computational and Applied Mathematics
Monotonic solution of heterogeneous anisotropic diffusion problems
Journal of Computational Physics
Hi-index | 31.47 |
Nonlinear constrained finite element approximations to anisotropic diffusion problems are considered. Starting with a standard (linear or bilinear) Galerkin discretization, the entries of the stiffness matrix are adjusted so as to enforce sufficient conditions of the discrete maximum principle (DMP). An algebraic splitting is employed to separate the contributions of negative and positive off-diagonal coefficients which are associated with diffusive and antidiffusive numerical fluxes, respectively. In order to prevent the formation of spurious undershoots and overshoots, a symmetric slope limiter is designed for the antidiffusive part. The corresponding upper and lower bounds are defined using an estimate of the steepest gradient in terms of the maximum and minimum solution values at surrounding nodes. The recovery of nodal gradients is performed by means of a lumped-mass L"2 projection. The proposed slope limiting strategy preserves the consistency of the underlying discrete problem and the structure of the stiffness matrix (symmetry, zero row and column sums). A positivity-preserving defect correction scheme is devised for the nonlinear algebraic system to be solved. Numerical results and a grid convergence study are presented for a number of anisotropic diffusion problems in two space dimensions.