An adaptive algorithm for the Crank-Nicolson scheme applied to a time-dependent convection-diffusion problem
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A multiphase-field model for the description of coalescence in a binary alloy is solved numerically using adaptive finite elements with high aspect ratio. The unknown of the multiphase-field model are the three phase fields (solid phase 1, solid phase 2, a ...
We consider a heterogeneous model for the dynamics of a blood solute both in the vascular lumen and inside the arterial wall. In the lumen, we consider an advection-diffusion equation, where the convective field is provided by the velocity of blood, which ...
In this paper we recall a stabilization technique for finite element methods for convection-diffusion-reaction equations, originally proposed by Douglas and Dupont. The method uses least square stabilization of the gradient jumps a across element boundarie ...
A posteriori error estimates for the heat equation in two space dimensions are presented. A classical discretization is used, Euler backward in time, and continuous, piecewise linear triangular finite elements in space. The error is bounded above and below ...
The computation of the reachable set of states of a given dynamic system is an important step to verify its safety during operation. There are different methods of computing reachable sets, namely interval integration, capture basin, methods involving the ...
A space–time adaptive method is presented for the numerical simulation of mass transport in electroosmotic and pressure-driven microflows in two space dimensions. The method uses finite elements with large aspect ratio, which allows the electroosmotic flow ...
The spatial step size for the second-order accurate Muskingum-Cunge (M-C) method is determined by the spatial weighting factor. Both the spatial weighting factor and the time step must be selected judiciously to obtain accurate solutions. In this study, ac ...