Wenju Zhao

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Verified

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• Doctor of Philosophy
• Professor (Associate) at Shandong University

In this paper, we propose a fully discrete numerical scheme for the Navier–Stokes equations, which combines the variable time step Dahlquist, Liniger, and Nevanlinna method in time and the symmetric interior penalty discontinuous Galerkin method in space. The proposed fully discrete numerical scheme satisfies the unconditional energy stability. We...

This paper presents a gradient-based approach for solving a switching time control problem under the two-phase porous media flow within petroleum extraction. The primary goal is to find an optimal switching time strategy that will maximize the net present value over a predetermined production period. To achieve this aim, a combination of Lagrangian...

In this paper, we study numerical methods for solving a class of nonlinear backward stochastic partial differential equations. By utilizing finite element methods in space and $\theta$-scheme in time, the proposed scheme forms a generalized spatio-temporal full discrete scheme, which can be solved in parallel. We rigorously prove the boundedness an...

This paper investigates reduced-order modeling of the Korteweg de Vries regularized long-wave Rosenau (KdV-RLW-Rosenau) equation using semi- and fully-discrete B-spline Galerkin approximations. The approach involves the application of a proper orthogonal decomposition (POD) method to a Galerkin finite element (GFE) formulation, resulting in a POD G...

In this paper, a scalar auxiliary variable approach combining with a discontinuous Galerkin method is proposed to handle the gradient‐type nonlinear term. The nonlinear convection–diffusion equation is used as the model. The proposed equivalent system can effectively handle the nonlinear convection term by incorporating the spatial and temporal inf...

This paper investigates the strong convergence of a fully discrete numerical method for the stochastic partial differential equations driven by multiplicative noise. The fully discrete space–time approximation consists of the symmetric interior penalty discontinuous Galerkin method for the spatial discretization and the implicit Euler method for th...

We consider the optimal control of a system governed by the Navier–Stokes equations with stochastic Dirichlet boundary conditions. Control conditions imposed only on the boundary are associated with reduced regularity of the system, as compared to distributed controls. To ensure the well-posedness of the solutions and the efficiency of numerical si...

In this paper, we construct and analyze the energy-stable weak Galerkin schemes for the Cahn–Hilliard equation in the mixed form. The energy stability depends on the newly defined discrete energy functional. We propose two robust weak Galerkin schemes with extra stabilizing terms in time: the first-order conditionally energy stable scheme of which...

This paper concerns an efficient finite element method for the natural convection equations with the scalar auxiliary variable approach. The linearly extrapolated Crank-Nicolson techniques are used to discretize nonlinear terms in the Navier–Stokes equations and the heat equation. The induced scalar auxiliary equation is an univariate ordinary equa...

This paper introduces a C0 weak Galerkin finite element method for a linear Cahn–Hilliard–Cook equation. The highlights of the proposed method are that the complexity of constructing the C1 finite element space for fourth order problem is avoided and the number of degree of freedom is apparently reduced compared to the fully discontinuous weak Gale...

In this article, we provide a class of numerical schemes to solve the steady state and non‐steady state Navier–Stokes equations with large Reynolds number. The high order weak Galerkin methods are numerically proposed and tested. We numerically find that the stabilizing term has a great impact on the robustness of the Jacobian matrices associated w...

An inverse spectral problem for Sturm–Liouville operators with frozen argument irrationally proportioned to the interval length is studied in this paper. We present a constructive procedure for reconstructing the potential from the spectrum.

The weak Galerkin form of the finite element method, requiring only C⁰ basis function, is applied to the biharmonic equation. The computational procedure is thoroughly considered. Local orthogonal bases on triangulations are constructed using various sets of interpolation points with the Gram-Schmidt or Levenberg-Marquardt methods. Comparison and h...

The authors present a constructive algorithm for the numerical solution to a class of the inverse transmission eigenvalue problem. The numerical experiments are provided to demonstrate the efficiency of our algorithms by a numerical example.

This paper is devoted to a newly developed weak Galerkin finite element method with the stabilization term for a linear fourth order parabolic equation, where weakly defined Laplacian operator over discontinuous functions is introduced. Priori estimates are developed and analyzed in L2 and an H2 type norm for both semi‐discrete and fully discrete s...

A weak-Galerkin finite element method is used to determine approximate solutions of an elliptic variational inequality. Three sets of basis functions are employed: the first has constant values inside each element and on each edge; the second has constant values inside each element but is a linear polynomial on each edge; and the third has linear p...

Performing stochastic inversion on a computationally expensive forward simulation model with a high-dimensional uncertain parameter space (e.g. a spatial random field) is computationally prohibitive even with gradient information provided. Moreover, the `nonlinear' mapping from parameters to observables generally gives rise to non-Gaussian posterio...

This paper is concerned with the finite element approximation of the stochastic Cahn–Hilliard–Cook equation driven by an infinite dimensional Wiener type noise. The Argyris finite elements are used to discretize the spatial variables while the infinite dimensional (cylindrical) Wiener process is approximated by truncated stochastic series spanned b...

In this paper we consider a non-autonomous ratio-dependent predator–prey system driven by Lévy noise. Firstly, we show the existence of global positive solution and stochastic boundedness. Secondly, the conditions of persistent in mean and extinction are established and we also give the asymptotic properties of the solution. Finally, we simulate th...

We consider stochastic suppression and stabilization for nonlinear delay differential system. The system is assumed to satisfy local Lipschitz condition and one-side polynomial growth condition. Since the system may explode in a finite time, we stochastically perturb this system by introducing independent Brownian noises and Lévy noise feedbacks. T...