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The drying shrinkage of porous materials is significantly dependent on external relative humidity (RHe$RH^{e}$). The perspective of temperature increase due to the climate change will accentuate the drying phenomenon in structures in lands and cities. The evolution of shrinkage can be determined by equivalent pore pressure consisting of capillary pressure Pc$P_c$, disjoining pressure and pressure caused by interfacial energy. For concrete structures, up to RHe=70%$RH^{e}=70 \%$ condition, standard models can reproduce the drying shrinkage experiments accurately. However, as the RHe$RH^{e}$ decreases to 30%, these models seem to be limited because the measured relationship (Pc−Sw${{P}_{c}}-{{S}_{w}}$) differs from the corresponding static equilibrium relationship as the drying occurs rapidly and the dynamic fluid flow effects on capillary pressure have been neglected. In this paper, the standard shrinkage model has been improved to take into account the dynamic flow effect and the viscoelastic behaviour of the solid skeleton. The dynamic and standard models have been compared with experimental results of drying shrinkage of concrete with two different relative humidity conditions. The standard model clearly showed its limitations at low external relative humidity RHe=30%$RH^{e}=30 \%$. However, the dynamic model showed good prediction of mass loss and shrinkage strains at high and low humidity conditions. Furthermore, the numerical and experimental investigations indicate that not only the dynamic effects but also the additional pressure induced by surface energy should be taken into account to quantify the drying shrinkage of cement‐based materials at low RHe$RH^{e}$ condition. [ABSTRACT FROM AUTHOR]

The monodomain model is a widely used model in electrocardiology to simulate the propagation of electrical potential in the myocardium. In this paper, we investigate a positive nonlinear control volume finite element scheme, based on Godunov's flux approximation of the diffusion term, for the monodomain model coupled to a physiological ionic model (the Beeler–Reuter model) and using an anisotropic diffusion tensor. In this scheme, degrees of freedom are assigned to vertices of a primal triangular mesh, as in conforming finite element methods. The diffusion term which involves an anisotropic tensor is discretized on a dual mesh using the diffusion fluxes provided by the conforming finite element reconstruction on the primal mesh and the other terms are discretized by means of an upwind finite volume method on the dual mesh. The scheme ensures the validity of the discrete maximum principle without any restriction on the transmissibility coefficients. By using a compactness argument, we obtain the convergence of the discrete solution and as a consequence, we get the existence of a weak solution of the original model. Finally, we illustrate by numerical simulations that the proposed scheme successfully removes nonphysical oscillations in the propagation of the wavefront and maintains conduction velocity close to physiological values. [ABSTRACT FROM AUTHOR]

In this article, a new numerical scheme for a degenerate Keller-Segel model with heterogeneous anisotropic tensors is treated. It is well-known that standard finite volume scheme not permit to handle anisotropic diffusion without any restrictions on meshes. Therefore, a combined finite volume-nonconforming finite element scheme is introduced, developed, and studied. The unknowns of this scheme are the values at the center of cell edges. Convergence of the approximate solution to the continuous solution is proved only supposing the shape regularity condition for the primal mesh. This scheme ensures the validity of the discrete maximum principle under the classical condition that all transmissibilities coefficients are positive. Therefore, a nonlinear technique is presented, as a correction of the diffusive flux, to provide a monotone scheme for general tensors. © 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 30: 1030-1065, 2014 [ABSTRACT FROM AUTHOR]