Related papers: New highly efficient and accurate numerical scheme…
This work aims to introduce a heuristic timestep-adaptive algorithm for Computational Fluid Dynamics (CFD) and Fluid-Structure Interaction (FSI) problems where the flow is dominated by the pressure. In such scenarios, many time-adaptive…
In this paper, we present a class of nonuniform time-stepping, high-order linear stabilized schemes that can preserve both the discrete energy stability and maximum-bound principle (MBP) for the time-fractional Allen-Cahn equation. To this…
We are interested in high-order linear multistep schemes for time discretization of adjoint equations arising within optimal control problems. First we consider optimal control problems for ordinary differential equations and show loss of…
In this paper we consider a linearized variable-time-step two-step backward differentiation formula (BDF2) scheme for solving nonlinear parabolic equations. The scheme is constructed by using the variable time-step BDF2 for the linear term…
We propose a novel class of temporal high-order parametric finite element methods for solving a wide range of geometric flows of curves and surfaces. By incorporating the backward differentiation formulae (BDF) for time discretization into…
In this paper we propose and analyze an energy stable numerical scheme for the Cahn-Hilliard equation, with second order accuracy in time and the fourth order finite difference approximation in space. In particular, the truncation error for…
In this research work, we propose a high-order time adapted scheme for pricing a coupled system of fixed-free boundary constant elasticity of variance (CEV) model on both equidistant and locally refined space-grid. The performance of our…
Efficient and energy stable high order time marching schemes are very important but not easy to construct for the study of nonlinear phase dynamics. In this paper, we propose and study two linearly stabilized second order semi-implicit…
In this article we present a refined convergence analysis for a second order accurate in time, fourth order finite difference numerical scheme for the 3-D Cahn-Hilliard equation, with an improved convergence constant. A modified backward…
We develop and analyze high-order ensemble schemes for the unsteady Navier--Stokes--Darcy system with uncertain initial conditions, forcing terms, hydraulic conductivity tensors, and Lions-Beavers-Joseph-Saffman interface conditions. The…
In this work, we introduce the time filtering technique to develop several innovative semi-discrete schemes in time for the Cahn-Hilliard-Navier-Stokes (CHNS) system. These schemes achieve second-order temporal accuracy while maintaining…
We present several first-order and second-order numerical schemes for the Cahn-Hilliard equation with discrete unconditional energy stability. These schemes stem from the generalized Positive Auxiliary Variable (gPAV) idea, and require only…
How to develop efficient numerical schemes while preserving the energy stability at the discrete level is a challenging issue for the three component Cahn-Hilliard phase-field model. In this paper, we develop first and second order temporal…
We construct first- and second-order time discretization schemes for the Cahn-Hilliard-Navier-Stokes system based on the multiple scalar auxiliary variables approach (MSAV) approach for gradient systems and (rotational) pressure-correction…
Due to the lack of corresponding analysis on appropriate mapping operator between two grids, high-order two-grid difference algorithms are rarely studied. In this paper, we firstly discuss the boundedness of a local bi-cubic Lagrange…
It is known in \cite{beccari} that the standard explicit Euler-type scheme (such as the exponential Euler and the linear-implicit Euler schemes) with a uniform timestep, though computationally efficient, may diverge for the stochastic…
In this report, we propose a new adaptive time filter algorithm for the unsteady Stokes/Darcy model. First we present a first order ${\theta}$-scheme with the variable time step which is one parameter family of Linear Multi-step methods and…
We consider a family of variable time-stepping Dahlquist-Liniger-Nevanlinna (DLN) schemes, which is unconditional non-linear stable and second order accurate, for the Allen-Cahn equation. The finite element methods are used for the spatial…
We develop and analyze a class of maximum bound preserving schemes for approximately solving Allen--Cahn equations. We apply a $k$th-order single-step scheme in time (where the nonlinear term is linearized by multi-step extrapolation), and…
In this paper, we present a novel second order in time mixed finite element scheme for the Cahn-Hilliard-Navier-Stokes equations with matched densities. The scheme combines a standard second order Crank-Nicholson method for the…