The scheme S with the standard-type spatial discretization
 has the form
However, the analysis and evaluation of discretization
behaviors in SMC systems has proved to be a difficult task due to the lack of work done on this topic.
In , we were inspired by looking at the time variable t in a parabolic problem as just another variable, say, [x.sub.d+1] if [x.sub.1],..., [x.sub.d] are the spatial variables, and at the time derivative as a strong convection in the direction [x.sub.d+1] that can numerically be treated in a stable way by special discretization
techniques known from convection-dominated elliptic convection-diffusion problems; see, e.g., .
For the DGFEM-0 spatial discretization
, Azmy estimated the residual using Taylor expansion and inverted the discrete transport operator using the residual as a source to estimate the error .
The variational discretization
approach is used to deal with the control and the error estimates are obtained in some norms.
(i) Whitney's discretization
, where a connection [theta] [member of] C(P) is integrated on the 1-vertices of the chosen triangulation.
With a robust method for inverting the Laplace transform we may then hybridize the transform with a discretization
Continuous models based on systems of ordinary or partial differential equations have been investigated under proper criteria of discretization
in this special issue.
The finite volume method (FVM) involves a spatial discretization
of the domain using a mesh.
As just described, applying the discretization
step of the data conversion process results in a presence-absence matrix with the same dimensions as the concentration matrix.
Caption: FIGURE 3: The RL spectrum of an MA-CDR array calculated at different discretization
step sizes (a), zoomed part of the RL spectrum (b), and top view of the CDR including the discretization
mesh at different levels in (c).
The rest of this paper is organized as follows: Section 2 presents the generation procedures of concrete mesostructure; the FE modeling methodology including mesh discretization
, insertion of ITZ elements, and constitutive modeling of mortar and ITZ is described in Section 3; in Section 4, the effects of voids on concrete tensile fracturing are discussed in detail based on the simulation results of several concrete specimens with different mesostructures; finally, the study is summarized with conclusions in Section 5.