SIAM Journal on Scientific and Statistical Computing
Singularities and similarities in interface flows
Trends and perspectives in applied mathematics
Symmetric singularity formation in lubrication-type equations for interface motion
SIAM Journal on Applied Mathematics
On the Cahn-Hilliard equation with degenerate mobility
SIAM Journal on Mathematical Analysis
Convergence of an Iterative Method for Total Variation Denoising
SIAM Journal on Numerical Analysis
A monotone finite element scheme for convection-diffusion equations
Mathematics of Computation
Positivity-Preserving Numerical Schemes for Lubrication-Type Equations
SIAM Journal on Numerical Analysis
Modelling of heat transport in magnetised plasmas using non-aligned coordinates
Journal of Computational Physics
Numerical Solution of Partial Differential Equations: An Introduction
Numerical Solution of Partial Differential Equations: An Introduction
Journal of Computational Physics
MOVCOL4: A Moving Mesh Code for Fourth-Order Time-Dependent Partial Differential Equations
SIAM Journal on Scientific Computing
On discrete maximum principles for nonlinear elliptic problems
Mathematics and Computers in Simulation
Preserving monotonicity in anisotropic diffusion
Journal of Computational Physics
Journal of Computational Physics
Discrete Maximum Principle and Adequate Discretizations of Linear Parabolic Problems
SIAM Journal on Scientific Computing
A mixed implicit-explicit finite difference scheme for heat transport in magnetised plasmas
Journal of Computational Physics
Journal of Computational Physics
Discrete maximum principle for linear parabolic problems solved on hybrid meshes
Applied Numerical Mathematics
SIAM Journal on Numerical Analysis
On maximum-principle-satisfying high order schemes for scalar conservation laws
Journal of Computational Physics
Journal of Computational Physics
SIAM Journal on Numerical Analysis
Hi-index | 31.45 |
The cutoff method, which cuts off the values of a function less than a given number, is studied for the numerical computation of nonnegative solutions of parabolic partial differential equations. A convergence analysis is given for a broad class of finite difference methods combined with cutoff for linear parabolic equations. Two applications are investigated, linear anisotropic diffusion problems satisfying the setting of the convergence analysis and nonlinear Lubrication-type equations for which it is unclear if the convergence analysis applies. The numerical results are shown to be consistent with the theory and in good agreement with existing results in the literature. The convergence analysis and applications demonstrate that the cutoff method is an effective tool for use in the computation of nonnegative solutions. Cutoff can also be used with other discretization methods such as collocation, finite volume, finite element, and spectral methods and for the computation of positive solutions.