This paper presents a sliding mode filter for removing noise. It effectively removes impulsive noise and high-frequency noise with producing smaller phase lag than linear filters. In addition, it is less prone to overshoot than previous sliding mode filters and it does not produce chattering. It is computationally inexpensive, and thus suitable for realtime applications. The proposed sliding mo...

We study the backward Euler fully discrete mixed finite element method for time-dependent Schrödinger equation; error result of solution is obtained in L2-norm with order O(τ+hk+1). Then, a two-grid presented scheme. Using this method, we solve original problem on much coarser grid and elliptic equations fine grid. In addition, also O(τ+hk+1+Hk+2). The numerical experiment provided to demonstra...

In this paper, a multi-point flux mixed-finite-element decoupled method was considered for the compressible miscible displacement problem. For problem, fully discrete backward Euler scheme proposed, in which velocity and pressure equations were by MFE using BDM1 elements combined with trapezoidal quadrature rule. The concentration equation handled standard FE method. error analysis velocity, pr...

In this paper, we consider the classical wave equation with time-dependent, spatially multiscale coefficients. We propose a fully discrete computational method in spirit of localized orthogonal decomposition space backward Euler scheme time. show optimal convergence rates and time beyond assumptions spatial periodicity or scale separation Further, an adaptive update strategy for time-dependent ...

We propose a numerical approximation method for the Cahn-Hilliard equations that incorporates continuous data assimilation in order to achieve long time accuracy. The uses C0 interior penalty spatial discretization of fourth equations, together with backward Euler temporal discretization. prove is stable and accurate, arbitrarily inaccurate initial conditions, provided enough measurements are i...

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We prove existence and numerical stability of numerical solutions of three fully discrete interior penalty discontinuous Galerkin (IPDG) methods for solving nonlinear parabolic equations. Under some appropriate regularity conditions, we give the l(H) and l(L) error estimates of the fully discrete symmetric interior penalty discontinuous Galerkin (SIPG) scheme with the implicit θ-schemes in time...

The long time numerical approximation of the parabolic p-Laplacian problem with a time-independent forcing term and sufficiently smooth initial data is studied. Convergence and stability results which are uniform for t ∈ [0,∞) are established in the L2, W 1,p norms for the backward Euler and the Crank–Nicholson schemes with the finite element method (FEM). This result extends the existing unifo...

We investigate analytically as well as numerically Burgers equation with a high-order nonlinearity (i.e., ut = νuxx−unux+mu+h(x)). We show existence of an absorbing ball in L2[0,1] and uniqueness of steady state solutions for all integer n ≥ 1. Then, we use an adaptive nonlinear boundary controller to show that it guarantees global asymptotic stability in time and convergence of the solution to...