Generalized SAV-exponential integrator schemes for Allen--Cahn type gradient flows
The energy dissipation law and the maximum bound principle (MBP) are two important
physical features of the well-known Allen--Cahn equation. While some commonly used first …
physical features of the well-known Allen--Cahn equation. While some commonly used first …
Analysis of adaptive BDF2 scheme for diffusion equations
H Liao, Z Zhang - Mathematics of Computation, 2021 - ams.org
The variable two-step backward differentiation formula (BDF2) is revisited via a new
theoretical framework using the positive semi-definiteness of BDF2 convolution kernels and …
theoretical framework using the positive semi-definiteness of BDF2 convolution kernels and …
Arbitrarily high-order exponential cut-off methods for preserving maximum principle of parabolic equations
A new class of high-order maximum principle preserving numerical methods is proposed for
solving parabolic equations, with application to the semilinear Allen--Cahn equation. The …
solving parabolic equations, with application to the semilinear Allen--Cahn equation. The …
Stabilized exponential-SAV schemes preserving energy dissipation law and maximum bound principle for the Allen–Cahn type equations
It is well-known that the Allen–Cahn equation not only satisfies the energy dissipation law
but also possesses the maximum bound principle (MBP) in the sense that the absolute value …
but also possesses the maximum bound principle (MBP) in the sense that the absolute value …
A third order BDF energy stable linear scheme for the no-slope-selection thin film model
Y Hao, Q Huang, C Wang - arXiv preprint arXiv:2011.01525, 2020 - arxiv.org
In this paper we propose and analyze a (temporally) third order accurate backward
differentiation formula (BDF) numerical scheme for the no-slope-selection (NSS) equation of …
differentiation formula (BDF) numerical scheme for the no-slope-selection (NSS) equation of …
Geometric quasilinearization framework for analysis and design of bound-preserving schemes
K Wu, CW Shu - SIAM Review, 2023 - SIAM
Solutions to many partial differential equations satisfy certain bounds or constraints. For
example, the density and pressure are positive for equations of fluid dynamics, and in the …
example, the density and pressure are positive for equations of fluid dynamics, and in the …
Analysis of the second-order BDF scheme with variable steps for the molecular beam epitaxial model without slope selection
In this work, we are concerned with the stability and convergence analysis of the second-
order backward difference formula (BDF2) with variable steps for the molecular beam …
order backward difference formula (BDF2) with variable steps for the molecular beam …
Simple positivity-preserving nonlinear finite volume scheme for subdiffusion equations on general non-conforming distorted meshes
X Yang, H Zhang, Q Zhang, G Yuan - Nonlinear Dynamics, 2022 - Springer
We propose a positivity-preserving finite volume scheme on non-conforming quadrilateral
distorted meshes with hanging nodes for subdiffusion equations, where the differential …
distorted meshes with hanging nodes for subdiffusion equations, where the differential …
Mesh-robustness of an energy stable BDF2 scheme with variable steps for the Cahn–Hilliard model
H Liao, B Ji, L Wang, Z Zhang - Journal of Scientific Computing, 2022 - Springer
The two-step backward differential formula (BDF2) with unequal time-steps is applied to
construct an energy stable convex-splitting scheme for the Cahn–Hilliard model. We focus …
construct an energy stable convex-splitting scheme for the Cahn–Hilliard model. We focus …
An implicit–explicit second-order BDF numerical scheme with variable steps for gradient flows
In this paper, we propose and analyze an efficient implicit–explicit second-order backward
differentiation formulation (BDF2) scheme with variable time steps for gradient flow problems …
differentiation formulation (BDF2) scheme with variable time steps for gradient flow problems …