Mixed time discontinuous space-time finite element method for convection diffusion equations

A mixed time discontinuous space-time finite element scheme for secondorder convection diffusion problems is constructed and analyzed. Order of the equation is lowered by the mixed finite element method. The low order equation is discretized with a space-time finite element method, continuous in space but discontinuous in time. Stability, existence, uniqueness and convergence of the approximate solutions are proved. Numerical results are presented to illustrate efficiency of the proposed method.

Time discontinuous Galerkin space-time finite element method for nonlinear Sobolev equations

This article presents a complete discretization of a nonlinear Sobolev equation using space-time discontinuous Galerkin method that is discontinuous in time and continuous in space. The scheme is formulated by introducing the equivalent integral equation of the primal equation. The proposed scheme does not explicitly include the jump terms in time, which represent the discontinuity characteristics of approximate solution. And then the complexity of the theoretical analysis is reduced. The existence and uniqueness of the approximate solution and the stability of the scheme are proved. The optimalorder error estimates in L2 （H1） and L2 （L2） norms are derived. These estimates are valid under weak restrictions on the space-time mesh, namely, without the condition kn ≥ ch2, which is necessary in traditional space-time discontinuous Galerkin methods. Numerical experiments are presented to verify the theoretical results.

Incubation time fracture criterion for FEM simulations

The paper is discussing problems connected with embedment of the incubation time criterion for brittle fracture into finite element computational schemes. Incubation time fracture criterion is reviewed; practical questions of its numerical implementation are extensively discussed. Several examples of how the incubation time fracture criterion can be used as fracture condition in finite element computations are given. The examples include simulations of dynamic crack propagation and arrest, impact crater formation （i.e. fracture in initially intact media）, spall fracture in plates, propagation of cracks in pipelines. Applicability of the approach to model initiation, development and arrest of dynamic fracture is claimed.

Hydration Process and Crack Tendency of Concrete Based on Resistivity and Restrained Shrinkage Crack

Hydration process, crack potential and setting time of concrete grade C30, C40 and C50 were monitored by using a non-contact electrical resistivity apparatus, a novel plastic ring mould and penetration resistance methods, respectively. The results show the highest resistivity of C30 at the early stage until a point when C50 accelerated and overtook the others. It has been experimentally confirmed that the crossing point of C30 and C50 corresponds to the final setting time of C50. From resistivity derivative curve, four different stages were observed upon which the hydration process is classified; these are dissolution, induction, acceleration and deceleration periods. Consequently, restrained shrinkage crack and setting time results demonstrated that C50 set and cracked the earliest. The cracking time of all the samples occurred within a reasonable experimental period thus the novel plastic ring is a convenient method for predicting concrete＇s crack potential. The highest inflection time（t_i） obtained from resistivity curve and the final setting time（t_f） were used with crack time（t_c） in coming up with mathematical models for the prediction of concrete＇s cracking age for the range of concrete grade considered. Finally, an ANSYS numerical simulation supports the experimental findings in terms of the earliest crack age of C50 and the crack location.