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Two High-Order Time Discretization Schemes for Subdiffusion Problems with Nonsmooth Data
Two new high-order time discretization schemes for solving subdiffusion problems with nonsmooth data are developed based on the corrections of the...
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An entropy stable finite volume method for a compressible two phase model
We study a binary mixture of compressible viscous fluids modelled by the Navier-Stokes-Allen-Cahn system with isentropic or ideal gas law. We propose...
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A Mixed Finite Element and Characteristic Mixed Finite Element for Incompressible Miscible Darcy-Forchheimer Displacement and Numerical Analysis
In this paper a mixed finite element-characteristic mixed finite element method is discussed to simulate an incompressible miscible Darcy-Forchheimer...
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Double stabilizations and convergence analysis of a second-order linear numerical scheme for the nonlocal Cahn-Hilliard equation
In this paper, we study a second-order accurate and linear numerical scheme for the nonlocal Cahn-Hilliard equation. The scheme is established by...
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Error Analysis of Nonlinear Time Fractional Mobile/Immobile Advection-Diffusion Equation with Weakly Singular Solutions
In this paper, a weighted and shifted Grünwald-Letnikov difference (WSGD) Legendre spectral method is proposed to solve the two-dimensional nonlinear...
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Simple maximum principle preserving time-step** methods for time-fractional Allen-Cahn equation
Two fast L1 time-step** methods, including the backward Euler and stabilized semi-implicit schemes, are suggested for the time-fractional...
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A Review on Variable-Order Fractional Differential Equations: Mathematical Foundations, Physical Models, Numerical Methods and Applications
Variable-order (VO) fractional differential equations (FDEs) with a time ( t ), space ( x ) or other variables dependent order have been successfully...
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Novel Numerical Analysis of Multi-Term Time Fractional Viscoelastic Non-Newtonian Fluid Models for Simulating Unsteady Mhd Couette Flow of a Generalized Oldroyd-B Fluid
In this paper, we consider the application of the finite difference method for a class of novel multi-term time fractional viscoelastic non-Newtonian...
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Error Estimates of High-Order Numerical Methods for Solving Time Fractional Partial Differential Equations
Error estimates of some high-order numerical methods for solving time fractional partial differential equations are studied in this paper. We first...
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A unified study of continuous and discontinuous Galerkin methods
A unified study is presented in this paper for the design and analysis of different finite element methods (FEMs), including conforming and...
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A Numerical Study of the Homogeneous Elliptic Equation with Fractional Boundary Conditions
We consider the homogeneous equation Au = 0, where A is a symmetric and coercive elliptic operator in H 1 (Ω) with Ω bounded domain in ℝ d . The boundary...
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An approach to construct higher order time discretisation schemes for time fractional partial differential equations with nonsmooth data
In this paper, we shall review an approach by which we can seek higher order time discretisation schemes for solving time fractional partial...
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Unconditional and optimal H 2-error estimates of two linear and conservative finite difference schemes for the Klein-Gordon-Schrödinger equation in high dimensions
The focus of this paper is on the optimal error bounds of two finite difference schemes for solving the d -dimensional ( d = 2, 3) nonlinear...
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A Novel Unstructured Mesh Finite Element Method for Solving the Time-Space Fractional Wave Equation on a Two-Dimensional Irregular Convex Domain
Most existing research on applying the finite element method to discretize space fractional operators is studied on regular domains using either...
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On the convergence of a second order approximation of conservation laws with discontinuous flux
A second order scheme is constructed for the scalar conservation laws with flux function allowed to be discontinuous in the space variable. The...
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A POD-based reduced-order finite difference extrapolating model for the non-stationary incompressible Boussinesq equations
A proper orthogonal decomposition (POD) method is used to establish a POD-based reduced-order finite difference (FD) extrapolating model with fully...
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Generation of Subordinated Holomorphic Semigroups via Yosida’s Theorem
Using functional calculi theory, we obtain several estimates for...
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An approximation scheme for the anisotropic and nonlocal mean curvature flow
In 2004 Chambolle proposed an algorithm for mean curvature flow based on a variational problem. Since then, the convergence, extensions and...
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A stabilized multi-level method for non-singular finite volume solutions of the stationary 3D Navier–Stokes equations
This paper proposes and analyzes a stabilized multi-level finite volume method (FVM) for solving the stationary 3D Navier–Stokes equations by using...
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A two-grid method with expanded mixed element for nonlinear reaction-diffusion equations
Expanded mixed finite element approximation of nonlinear reaction-diffusion equations is discussed. The equations considered here are used to model...