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961.
We develop a method for adaptive mesh refinement for steady state problems that arise in the numerical solution of Cahn–Hilliard equations with an obstacle free energy. The problem is discretized in time by the backward-Euler method and in space by linear finite elements. The adaptive mesh refinement is performed using residual based a posteriori estimates; the time step is adapted using a heuristic criterion. We describe the space–time adaptive algorithm and present numerical experiments in two and three space dimensions that demonstrate the usefulness of our approach. 相似文献
962.
This paper considers the problem of optimizing a continuous nonlinear objective function subject to linear constraints via a piecewise-linear approximation. A systematic approach is proposed, which uses a lattice piecewise-linear model to approximate the nonlinear objective function on a simplicial partition and determines an approximately globally optimal solution by solving a set of standard linear programs. The new approach is applicable to any continuous objective function rather than to separable ones only and could be useful to treat more complex nonlinear problems. A numerical example is given to illustrate the practicability. 相似文献
963.
A hyperbolic problem with volume constraint is investigated by means of a minimizing method called the discrete Morse flow. A weak solution is introduced in a constructive way and results of numerical computations are shown. 相似文献
964.
In this paper, we consider semilinear elliptic systems with both singular and critical growth terms in bounded domains. The existence of a nontrivial solution is obtained by variational methods. 相似文献
965.
A new, straightforward and systematic approach to construct rational-exponential solutions is proposed. The method is based on the formal perturbation theory. Explicit rational-exponential solutions for the two-dimensional elliptic sine-Gordon and Korteweg-de Vries equations are constructed. The method used is quite general and applicable to most nonlinear evolution equations, including certain multidimensional equations. 相似文献
966.
As to the Cauchy problem for the spatially inhomogeneous Boltzmann equation with cut-off, we prove uniform stability estimates for solutions and their gradients in a unified and elementary way. 相似文献
967.
This paper studies online scheduling problems with reassignment on two identical machines. We can reassign some jobs under certain rules after all the jobs have been assigned. Three different versions are studied and optimal algorithms are proposed. 相似文献
968.
The Fisher information of the classical orthogonal polynomials with respect to a parameter is introduced, its interest justified and its explicit expression for the Jacobi, Laguerre, Gegenbauer and Grosjean polynomials found. 相似文献
969.
The dependence of the linear stability of two-time-level finite-difference semi-implicit schemes on the choice of reference temperature profile is studied. Particular vertical profiles of the temperature are considered to derive analytical conditions of stability. Analysis is made for general form of different model parameters such as the number of vertical levels and their distribution, the time step size, and the values of the viscosity coefficients. The derived conditions of stability are more restrictive than those for three-time-level schemes, but obtained necessary and sufficient condition for constant vertical lapse rates of the temperature has the form frequently applied to three-time-level schemes: the basic temperature profile should be warmer than the actual one. Performed numerical experiments show that the last restriction is neither necessary nor sufficient condition of stability for general temperature profiles. 相似文献
970.