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Pinning adaptive anti-synchronization between two general complex dynamical networks with non-delayed and delayed coupling
Based on Lyapunov stability theory and Barbalat lemma, a sufficient condition is derived to guarantee the AS between two networks with non-delayed and delayed coupling. Expand
A modified Crank-Nicolson scheme with incremental unknowns for convection dominated diffusion equations
A modified Crank-Nicolson scheme based on one-sided difference approximations is proposed for solving time-dependent convection dominated diffusion equations in two-dimensional space. The modifiedExpand
Incremental unknowns in three-dimensional stationary problem
The main purpose of this work is to set up the explicit matrix framework appropriate to three-dimensional partial differential equations by means of the incrementalunknowns method, and it is confirmed that the incremental unknowns method is efficient and the hierarchical preconditioning based on the incremental Unknowns can be applied in a more general form. Expand
Interior penalty discontinuous Galerkin methods with implicit time‐integration techniques for nonlinear parabolic equations
We prove existence and numerical stability of numerical solutions of three fully discrete interior penalty discontinuous Galerkin methods for solving nonlinear parabolic equations. Under someExpand
Incremental unknowns method based on the theta-scheme for time-dependent convection-diffusion equations
A θ-scheme using two-level incremental unknowns is presented and numerical results of the convection-diffusion equations are investigated and confirm that oscillations can be controlled by the incrementalunknowns method. Expand
Fully Discrete Interior Penalty Discontinuous Galerkin Methods for Nonlinear Parabolic Equations
In this article, we investigate interior penalty discontinuous Galerkin (IPDG) methods for solving a class of two-dimensional nonlinear parabolic equations. For semi-discrete IPDG schemes on aExpand
Polynomial preserving recovery of an over-penalized symmetric interior penalty Galerkin method for elliptic problems
A polynomial preserving recovery technique is applied to an over-penalized symmetric interior penalty method. The discontinuous Galerkin solution values are used to recover the gradient and toExpand
Convergence of a Second-Order Linearized BDF–IPDG for Nonlinear Parabolic Equations with Discontinuous Coefficients
We study the anti-symmetric interior over-penalized discontinuous Galerkin finite element methods for solving nonlinear parabolic interface problems with second-order backward difference formula forExpand
This paper is concerned with a multi-domain spectral method, based on an interior penalty discontinuous Galerkin (IPDG) formulation, for the exterior Helmholtz problem truncated via an exact circularExpand
A family of interior-penalized weak Galerkin methods for second-order elliptic equations
Interior-penalized weak Galerkin (IPWG) finite element methods are proposed and analyzed for solving second order elliptic equations. The new methods employ the elementExpand