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This paper is concerned with the analysis and numerical solution of an $\boldsymbol {H}({\textbf {curl}})$-elliptic hemivariational inequality (HVI). One source of the HVI is through a temporal semidiscretization of a related hyperbolic Maxwell equation problem. An equivalent minimization principle is introduced, and the solution existence and uniqueness of the $\boldsymbol {H}({\textbf {curl}})$-elliptic HVI are proved. Numerical analysis of the HVI is provided with a general Galerkin approximation, including a Céa’s inequality for convergence and error estimation. When the linear edge finite element method is employed, an optimal-order error estimate is derived under a suitable solution regularity assumption. A fully discrete scheme based on the backward Euler difference in time and a mixed finite element method in space is also analyzed, and stability estimates are derived for first-order terms of the fully discrete solution. Numerical results are reported on linear edge finite element solutions of the $\boldsymbol {H}({\textbf {curl}})$-elliptic HVI for numerical evidence of the theoretically predicted convergence order.

This paper provides a well-posedness analysis for a hemivariational inequality of the stationary Navier-Stokes equations by arguments of convex minimization and the Banach fixed point. The hemivariational inequality describes a stationary incompressible fluid flow subject to a nonslip boundary condition and a Clarke subdifferential relation between the total pressure and the normal component of the velocity. Auxiliary Stokes hemivariational inequalities that are useful in proving the solution existence and uniqueness of the Navier–Stokes hemivariational inequality are introduced and analyzed. This treatment naturally leads to a convergent iteration method for solving the Navier–Stokes hemivariational inequality through a sequence of Stokes hemivariational inequalities. Equivalent minimization principles are presented for the auxiliary Stokes hemivariational inequalities which will be useful in developing numerical algorithms.

The diffusive-viscous wave equation arises in a variety of applications in geophysics, and it plays an important role in seismic exploration. In this paper, semi-discrete and fully discrete numerical methods are introduced to solve a general initial-boundary value problem of the diffusive-viscous wave equation. The spatial discretization is carried out through the finite element method, whereas the time derivatives are approximated by finite differences. Optimal order error estimates are derived for the numerical methods. Numerical results on a test problem are reported to illustrate the numerical convergence orders.

Aims: Protection of cardiac function following myocardial infarction was largely enhanced by bradykinin-pretreated cardiac-specific c-kit+ (BK-c-kit+) cells, even without significant engraftment, indicating that paracrine actions of BK-c-kit+ cells play a pivotal role in angiogenesis. Nevertheless, the active components of the paracrine actions of BK-c-kit+ cells and the underlying mechanisms remain unknown. This study aimed to define the active components of exosomes from BK-c-kit+ cells and elucidate their underlying protective mechanisms. Methods and results: Matrigel tube formation assay, cell cycle, and mobility in human umbilical vein endothelial cells (HUVECs) and hindlimb ischemia (HLI) in mice were applied to determine the angiogenic effect of condition medium (CM) and exosomes. Proteome profiler, microRNA sponge, Due-luciferase assay, microRNA-sequencing, qRT-PCR, and Western blot were used to determine the underlying mechanism of the angiogenic effect of exosomes from BK-c-kit+. As a result, BK-c-kit+ CM and exosomes promoted tube formation in HUVECs and the repair of HLI in mice. Angiogenesis-related proteomic profiling and microRNA sequencing revealed highly enriched miR-3059-5p as a key angiogenic component of BK-c-kit+ exosomes. Meanwhile, loss- and gain-of-function experiments revealed that the promotion of angiogenesis by miR-3059-5p was mainly through suppression of TNFSF15 (VEGI)-inhibited effects on vascular tube formation, cell proliferation and cell migration. Moreover, enhanced angiogenesis of miR-3059-5p-inhibited TNFSF15 has been associated with Akt/Erk1/2/Smad2/3-modulated signaling pathway. Conclusion: Our results demonstrated a novel finding that BK-c-kit+ cells enrich exosomal miR-3059-5p to suppress TNFSF15 and promote angiogenesis against hindlimb ischemia in mice.

We study a mixed discontinuous Galerkin (MDG) method for solving a time-dependent Darcy problem, which simulates an incompressible fluid such as water flowing in a rigid porous medium. The discreti...

In this paper, numerical analysis is carried out for a class of history-dependent variational-hemivariational inequalities arising in contact problems. Three different numerical treatments for temporal discretization are proposed to approximate the continuous model. Fixed-point iteration algorithms are employed to implement the implicit scheme and the convergence is proved with a convergence rate independent of the time step-size and mesh grid-size. A special temporal discretization is introduced for the history-dependent operator, leading to numerical schemes for which the unique solvability and error bounds for the temporally discrete systems can be proved without any restriction on the time step-size. As for spatial approximation, the finite element method is applied and an optimal order error estimate for the linear element solutions is provided under appropriate regularity assumptions. Numerical examples are presented to illustrate the theoretical results., 33 pages,6 figures

In this paper, an alternative approach is provided in the well-posedness analysis of elliptic variational–hemivariational inequalities in real Hilbert spaces. This includes the unique solvability and continuous dependence of the solution on the data. In most of the existing literature on elliptic variational–hemivariational inequalities, well-posedness results are obtained by using arguments of surjectivity for pseudomonotone multivalued operators, combined with additional compactness and pseudomonotonicity properties. In contrast, following (Han in Nonlinear Anal B Real World Appl 54:103114, 2020; Han in Numer Funct Anal Optim 42:371–395, 2021), the approach adopted in this paper is based on the fixed point structure of the problems, combined with minimization principles for elliptic variational–hemivariational inequalities. Consequently, only elementary results of functional analysis are needed in the approach, which makes the theory of elliptic variational–hemivariational inequalities more accessible to applied mathematicians and engineers. The theoretical results are illustrated on a representative example from contact mechanics.

Hemivariational inequalities arise in nonsmooth mechanics of solid involving nonmonotone and multi-valued mechanical relations. Typically, after the finite-element discretization, they lead to cons...

A Dy3+-doped PbGa2S4 crystal with low phonon energy has been proved to be able to achieve the direct lasing of a mid-infrared laser. The single-crystal growth of Dy3+:PbGa2S4 was investigated in th...

In the development process of oil and gas field, the dip angles generally exist in deep strata, and the variability and dispersion in the mechanics parameters of the formation make the computation model of in situ stress for a gentle structure no longer applicable. In light of the fact that the dip angle was large and the geological structure was complex in Sichuan basin and Xinjiang basin, uncertainty of mechanical parameters and tectonic stress coefficients of the formation were analyzed by the Monte Carlo method based on acoustic logging data and stratigraphic dipmeter log data. Taking dip angle and dip direction into account, the uncertainty calculation method for in situ stress in deep inclined strata was proposed. Multi-factor analysis was used to analyze the sensitivity of various factors affecting the in situ stress in deep inclined strata. The results show that, the horizontal in situ stress calculation model adopted in this paper is more suitable for structurally intense areas. The horizontal stress confidence interval is more significant for oil and gas field engineering than single principal stress value. For PY gas field and TLM oil field with different geological conditions and rocks mechanical parameters of formation, the dip angle and effective stress coefficient are the most sensitive to the horizontal in situ stress.

In this paper, we provide stability analysis for a stationary Stokes hemivariational inequality where along the tangential direction of the slip boundary, an inclusion relation involving the generalized subdifferential of a superpotential is specified. With viscous incompressible fluid flows as application background, stability is analyzed for solutions with respect to perturbations in the superpotential and the density of external forces. We also present a result on the existence of a solution to an optimal control problem for the stationary Stokes hemivariational inequality.

In this paper, we provide a comprehensive stability analysis for stationary variational inequalities, hemivariational inequalities, and variational-hemivariational inequalities. With contact mechanics as application background, stability is analyzed for solutions with respect to combined or separate perturbations in constitutive relations, external forces, constraints, and non-smooth contact boundary conditions of the inequality problems. The stability result is first proved for a general variational-hemivariational inequality. Then, stability results are obtained for various variational inequalities and hemivariational inequalities as special cases. Finally, we illustrate applications of the theoretical results for the stability analysis of model problems in contact mechanics.

This paper is on the numerical solution of an elliptic hemivariational inequality by the virtual element method. We introduce an abstract framework of the numerical method and provide an error analysis. We then apply the virtual element method to solve two contact problems: a bilateral contact problem with friction and a frictionless normal compliance contact problem. Error estimates of their numerical solutions are derived, which are of optimal order for the linear virtual element method, under appropriate solution regularity assumptions. The discrete problem can be formulated as an optimization problem for a difference of two convex (DC) functions, and a convergent algorithm is introduced to solve it. Numerical examples are reported to show the performance of the proposed methods.

In this paper, we consider the numerical solution of an evolutionary variational–hemivariational inequality arising in a dynamic contact problem. The material is assumed to be viscoelastic with short memory. The contact is featured by a normal damped response in the normal direction and by the Tresca friction law in the tangential direction. The linear finite elements are used to discretize the spatial variable. Optimal order error estimates are derived for the discrete velocity and discrete displacement under suitable solution regularity assumptions.

In this paper, we revisit the numerical solution of the scalar second-order wave equation by discontinuous Galerkin methods. The numerical methods are different from the ones found in existing lite...