Numerical simulation of oil-water miscible displacement is discussed in this paper, and a compressible problem of energy mathematics is solved potentially. The mathematical model defined by a ...nonlinear system includes mainly two partial differential equations (PDEs): a parabolic equation for the pressure and a convection-diffusion equation for the saturation. The pressure is obtained by a conservative mixed finite volume element method (MFVE). The computational accuracy is improved for Darcy velocity. A conservative upwind mixed finite volume element method (UMFVE) is applied to compute the saturation on changing meshes. The diffusion is discretized by a mixed finite volume element method, and the convection is computed by upwind differences. The upwind method can solve convection-dominated diffusion equations accurately and avoids numerical dispersion and nonphysical oscillation. The saturation and the adjoint vector function are obtained simultaneously. An optimal order error estimates is obtained. Finally, numerical examples are provided to show the accuracy, efficiency and possible applications.
This article presents a third-order backward differentiation formula (BDF3) finite difference scheme for the generalized viscous Burgers’ equation. The discretization of time and space directions is ...accomplished by the BDF3 method and standard second-order difference formula, respectively, thereby constructing a fully-discrete scheme. For the proposed scheme, we yield the convergence of h2+τ3 by means of the energy argument and the cut-off function method. Besides, a comparison of the time convergence rate and numerical accuracy with those of recent existing work shows the effectiveness and competitiveness of our approach. A numerical experiment is carried out to verify the theoretical predictions.
In this short note, we consider some issues regarding the instability of some elastodynamical problems when the elasticity tensor is not positive definite. By using the so-called logarithmic ...convexity argument, we prove the instability of solutions when the time derivative of the elasticity tensor is semi-definite negative or it satisfies another restriction on the coefficients. The uniqueness of the solution is also concluded. Finally, a simple one-dimensional example is provided to demonstrate the numerical behaviour of the instability.
•An incremental problem in elastodynamics is mathematically studied.•Instability is analyzed by using the logarithmic convexity argument.•Uniqueness of the solution is also considered.•A numerical example is performed to demonstrate the behaviour.
In this paper, we introduce a modified Krasnoselski–Mann type method for solving the hierarchical fixed point problem and split monotone variational inclusions in real Hilbert spaces. We prove that ...the sequence generated by the modified algorithm converges strongly to a common element of the set of hierarchical fixed point problem and split monotone variational inclusions only basing on the coefficients. Our results extend and improve the weak convergence results of Kazmi et al. (Kazmi et al., 2018) and others. Moreover, an application and its numerical examples illustrate the feasibility and strong convergence of the proposed method and results.
This paper deals with the analytical solution of the non-homogeneous, orthotropic right-angle triangle cross-section. The shear moduli of the elastic materials are linear function of the elastic ...materials are linear functions of the cross-sectional coordinates. Explicit formulas are given for Prandtl’s stress function, torsion function, shearing stresses, and torsional rigidity. The formulation of the solution is based on Saint-Venant’s theory of uniform torsion and the application of Prandtl’s stress function.
In this study, a Galerkin finite element method is presented for time-fractional stochastic heat equation driven by multiplicative noise, which arises from the consideration of heat transport in ...porous media with thermal memory with random effects. The spatial and temporal regularity properties of mild solution to the given problem under certain sufficient conditions are obtained. Numerical techniques are developed by the standard Galerkin finite element method in spatial direction, and Gorenflo–Mainardi–Moretti–Paradisi scheme is applied in temporal direction. The convergence error estimates for both semi-discrete and fully discrete schemes are established. Finally, numerical example is provided to verify the theoretical results.
This article describes the deformation analysis approach with robust methods in geodetic networks. The characteristic of this approach is the iterative weighted similarity transformation in which the ...displacement vector d is transformed into a datum determined by points with a smaller coordinate difference between two epochs. The article first gives a theoretical background of the approach, and then the approach is applied to the case of simulated measurements in two epochs. The calculated results of the deformation analysis approach with the robust methods in the present case do not differ significantly from the results obtained by conventional deformation analysis approaches.
This paper, we study a space-time continuous Galerkin (STCG) method with mesh change for two-dimensional (2-D) pseudo-hyperbolic equations with variable coefficients, which gives the same treatment ...for time and space discretizations, namely both time and space variables are discretized via finite element (FE) method. In addition, it allows the change of time step and space mesh which are necessary for adaptive algorithms. We prove the existence and uniqueness of approximation solution and give a prior error estimate without any conditions attached to the space-time grid. Finally, a numerical example is given to confirm the feasibility to the scheme constructed here.
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