Durmaz, Muhammet EnesCakir, MusaAmirali, IlhameAmiraliyev, Gabil M....
15页
查看更多>>摘要：This work presents a computational approximate to solve singularly perturbed Fredholm integro-differential equation with the reduced second type Fredholm equation. This problem is discretized by a finite difference approximate, which generates second-order uniformly convergent numerical approximations to the solution. Parameter-uniform approximations are generated using Shishkin type meshes. The performance of the numerical scheme is tested which supports the effectiveness of the technique. (c) 2022 Elsevier B.V. All rights reserved.
查看更多>>摘要：A new conforming discontinuous Galerkin method, which is based on weak Galerkin finite element method, is introduced for solving second order elliptic interface problems with discontinuous coefficient. The numerical method studied in this paper has no stabilizer and fewer unknowns compared with the known weak Galerkin algorithms. The error estimates in H-1 and L-2 norms are established, which are the optimal order convergence. Numerical experiments demonstrate the performance of the method, confirm the theoretical results of accuracy. (c) 2022 Elsevier B.V. All rights reserved.
查看更多>>摘要：In this article, we study a posteriori error analysis of quadratic finite element method in the maximum norm for the elliptic obstacle problem. We discuss the reliability and the efficiency of the proposed a posteriori error estimator. In the analysis, regularized Green's function plays a crucial role and together with that, in obtaining the sign of the discrete Lagrange multiplier we have exploited the property that midpoint quadrature rules are exact for quadratic polynomials. Numerical results are performed to illustrate the convergence behavior of a posteriori error estimator through various test examples. (c) 2022 Elsevier B.V. All rights reserved.
查看更多>>摘要：We consider mixed finite element approximation of a singularly perturbed fourth-order elliptic problem with two different boundary conditions, and present a new measure of the error, whose components are balanced with respect to the perturbation parameter. With different boundary conditions, the simply supported plate model and the clamped plate model are considered. In particular, a balanced energy norm has been defined. Based on the new norm, residual-based a posteriori estimators are developed for both problems, which are uniform with respect to both the perturbation parameter and the mesh function. A novel analysis approach is introduced for the clamped plate model to address certain difficulty of the problem. Numerical examples are provided to confirm theoretical findings. (c) 2022 Elsevier B.V. All rights reserved.
查看更多>>摘要：Distinguished from the existing HIV/AIDS epidemic models, we formulate a model by considering three-age-structured, spacial diffusion, viral load-dependent infection and conversion rates to study the global dynamical behaviors of HIV/AIDS transmission. The generation operator R and the explicit expression of basic reproduction ratio R-0 are introduced. The global stability of steady states and the uniform persistence of the disease are presented. Sensitivity analysis indicates that some parameters impact the value of R-0 markedly and the intervening measure plays a crucial role in the intervention of HIV infection at population level. Furthermore, numerical simulations suggest that intervening measure at the individual and population levels is highly effective in controlling the transmission of the disease. (c) 2022 Elsevier B.V. All rights reserved.
查看更多>>摘要：A new approach to the numerical simulation of the reaction front motion in a nonlinear singularly perturbed partial differential equation of the reaction-diffusion type is proposed. It is shown how the methods of asymptotic analysis allow reducing the statement of the original problem to a problem of a smaller dimension, the numerical solving of which uses methods of diagnostics of the solution's blow-up. Numerical experiments demonstrate the effectiveness of the proposed approach. (C) 2022 Elsevier B.V. All rights reserved.
查看更多>>摘要：We present important improvements and additions to a modern technique developed by Ixaru to solve the time-dependent two-dimensional Schrodinger equation with homogeneous Dirichlet boundary conditions over a rectangular domain. The algorithm, first described in Ixaru (2010), is based on the so-called Constant Perturbation technique. In this paper, we refine and extend the algorithm with important features. We focus in particular on new algorithms for the determination of the index of the eigenvalues, for the orthonormalization of eigenfunctions, for automatic step size selection and for the accurate computation of integrals. We provide the new developments with sufficient theoretical background and numerical experiments. (c) 2022 Elsevier B.V. All rights reserved.
查看更多>>摘要：We present here a numerical scheme based on the classical SIMPLE algorithm for the time-stepping and on a MAC discretization on staggered meshes for the estimation of the spatial derivatives. This scheme is applied here to a two-layer two-fluid model that has been proposed in previous works of the literature in order to perform computations of gas-liquid flows in pipes with gravity effects. This model accounts for pressure relaxation and velocity relaxation between the two phases through source terms. Thanks to new forms of these source terms, their discretization can be easily introduced in the different steps of the SIMPLE algorithm. The whole algorithm then allows to couple convective terms and source terms without suffering from the CFL limitation of the explicit Godunov-type schemes. A detailed description of the scheme is proposed and some numerical tests have been performed in order to assess the behavior of the approximated solutions when pressure-velocity relaxation is taken into account. (c) 2022 Elsevier B.V. All rights reserved.
查看更多>>摘要：We compare the long-time error bounds and spatial resolution of finite difference methods with different spatial discretizations for the Dirac equation with small electromagnetic potentials characterized by epsilon is an element of (0, 1] a dimensionless parameter. We begin with the simple and widely used finite difference time domain (FDTD) methods, and establish rigorous error bounds of them, which are valid up to the time at O(1/epsilon). In the error estimates, we pay particular attention to how the errors depend explicitly on the mesh size h and time step r as well as the small parameter epsilon. Based on the results, in order to obtain "correct "numerical solutions up to the time at O(1/epsilon), the epsilon-scalability (or meshing strategy requirement) of the FDTD methods should be taken as h = O(epsilon(1/2)) and r = O(epsilon(1/2)). To improve the spatial resolution capacity, we apply the Fourier spectral method to discretize the Dirac equation in space. Error bounds of the resulting finite difference Fourier pseudospectral (FDFP) methods show that they exhibit uniform spatial errors in the long-time regime, which are optimal in space as suggested by the Shannon's sampling theorem. Extensive numerical results are reported to confirm the error bounds and demonstrate that they are sharp. Published by Elsevier B.V.
查看更多>>摘要：In this work, we consider multigoal-oriented error estimation for stationary fluid-structure interaction. The problem is formulated within a variational-monolithic setting using arbitrary Lagrangian-Eulerian coordinates. Employing the dual-weighted residual method for goal-oriented a posteriori error estimation, adjoint sensitivities are required. For multigoal-oriented error estimation, a combined functional is formulated such that several quantities of interest are controlled simultaneously. As localization technique for mesh refinement we employ a partition-of-unity. Our algorithmic developments are substantiated with several numerical tests such as an elastic lid-driven cavity with two goal functionals, an elastic bar in a chamber with two goal functionals, and the FSI-1 benchmark with three goal functionals. (c) 2022 Elsevier B.V. All rights reserved.
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