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In this paper, we study a dynamic contact problemwith Clarke subdifferential boundaryconditions. The material is assumed to be viscoplastic which has an implicit expression of the stress field in constitutive law. The weak form of the model is governed by an evolutionaryhemivariational inequality coupled with an integral equation.We study a fully discrete approximation scheme of the problem and bound the errors. Under appropriate solution regularity assumptions, optimal-order error estimates can be derived. Finally, a numerical example is also included to support our theoretical analysis. Particularly, it gives numerical evidence on the theoretically predicted optimal convergence order.

This paper brings out an analysis of the projection iterative algorithm for the numerical solution of the Signorini problem. The very closed connections with the switching method are highlighted. In addition, the relevance of higher-order discretization for Signorini problem is discussed. Thus, a specific iterative solver is developed to address the present fourth and sixth-order compact scheme discretizations. This method is based on a lower-order preconditioning method. Several numerical experiments have been performed to bring light to the accuracy of such method, despite the lack of smoothness at the Signorini boundary.

In this paper, we study a parameter identification problem for elliptic partial differential equations. We reconstruct the coefficient with additional boundary measurements, including both Dirichle...

In this paper, we propose an iterative algorithm for a simplified friction problem which is formulated as an elliptic variational inequality of the second kind. We approximate the simplified friction problem by a discrete system with the finite element method. Based on the use of the linearized technique and by constructing a particular function, we put forward the new algorithm to get the discrete solution. This algorithm is attractive due to its simple proof of convergence and easy implementation. A linear equation is solved in each iteration. Numerical results confirm that our algorithm is efficient and mesh independent.

In this paper, we derive the piecewise linear system PLS associated with the bilateral obstacle problem and illustrate the equivalence between the linear system and finite-dimensional complementary problem. The existence and the uniqueness of the solution to the PLS are also demonstrated. Based on the PLS, a Picard iterative algorithm is proposed. The convergence analysis is given and examples are presented to verify the effectiveness of the method.

In this paper, we discuss the numerical method for solving the first kind of elliptic variational inequality. We first use the fundamental solution as the basis function to approximate the solution of variational inequality, then we employ Uzawa's algorithm to determine the free boundary and the solution. Numerical examples are given to verify the efficiency of the method.

The premixed turbulent V-flame is numerically simulated in this paper. The technique used in Chan et al. [Effect of intense turbulence on turbulent premixed V-flame, Int. J. Eng. Sci. 41 (2003), pp. 903-916; Simulation of a premixed turbulent flame with the discrete vortex method, Int. J. Numer. Methods Eng. 48 (2000), pp. 613-627] was based on the random vortex method and the conventional level set method. However, this paper is an improvement of the previous technique by using a conservative level set method. The new algorithm uses a bi-cubic interpolation process together with Newton's method to reconstruct the velocity field to improve the conservation of the level set method. The numerical example in this paper indicates the efficiency of the new method in solving the problem of turbulent premixed V-flame by comparing the results with available data.

In this paper, a linearly semi-implicit compact scheme is developed for the Burgers-Huxley equation. The equation is decomposed into two subproblems, i.e. a Burgers equation and a nonlinear ODE, by the operator splitting technique. The Burgers equation is solved by a linearly self-starting compact scheme which is fourth-order accurate in space and second-order accurate in time. The nonlinear ODE is discretized by a third-order semi-implicit Runge-Kutta method, which possesses good numerical stability with low computational cost. The numerical experiments show that the scheme provides the expected convergence order. Finally, several experiments are conducted to simulate the solutions of the Burgers-Huxley equation to validate our numerical method.

This paper studies the eigenvalue optimization problems in the shape design of the two-density inhomogeneous materials. Two types of greedy algorithms are proposed to solve three optimization problems in finite element discretization. In the first type, the whole domain is initialized by one density. For each problem of the eigenvalue optimizations, we define a measurement of the element, which is the criterion to determine the 'best' element. We change the density of the 'best' element to the other density. Then the algorithm repeats the procedure until the area constraint is satisfied. In the second type, the algorithm begins with the density distribution satisfying the area constraint. Also, according to the measurement of the element, the algorithm finds a pair of the 'best' elements and exchanges their densities between each other. Furthermore, the accelerating greedy algorithms are proposed to speed up both two types. Three numerical examples are provided to illustrate the results.

In this paper we propose some iterative algorithms for the obstacle problems discretized by the finite difference method. We rewrite the obstacle problem to an equivalent complementarity problem. We use the regularization trick to non-smooth absolute function. Then we apply the Newton's method to obtain an iterative algorithm. Some other two algorithms based on this algorithm are derived. Numerical experiments show the effective of the algorithm.

In this paper, we propose an iterative algorithm based on the level set method for the shape recovery problem. We use a suitable preconditioner for the artificial time-dependent system for the level set formulation and propose an iterative algorithm of the level set function. We prove the convergence of our algorithm under some hypothesis. Numerical experiments show the efficiency of the algorithm.