In this work we consider the dual-primal Discontinuous Petrov–Galerkin (DPG) method for the advection-diffusion model problem. Since in the DPG method both mixed internal variables are discontinuous, a static condensation procedure can be carried out, leading to a single-field nonconforming discretization scheme. For this latter formulation, we propose a flux-upwind stabilization technique to deal with the advection-dominated case. The resulting scheme is conservative and satisfies a discrete maximum...
In this articlewe address the study of ion charge transport in the biological channels separating the intra and extracellular regions of a cell. The focus of the investigation is devoted to including thermal driving forces in the well-known velocity-extended Poisson-Nernst-Planck (vPNP) electrodiffusion model. Two extensions of the vPNP system are proposed: the velocity-extended Thermo-Hydrodynamic model (vTHD) and the velocity-extended Electro-Thermal model (vET). Both formulations are based on...
In this work we consider the
dual-primal Discontinuous Petrov–Galerkin (DPG)
method for the advection-diffusion model problem.
Since in the DPG method both
mixed internal variables are discontinuous,
a static condensation procedure can be
carried out, leading to a single-field nonconforming
discretization scheme. For this latter formulation,
we propose a flux-upwind stabilization technique to deal with
the advection-dominated case.
The resulting scheme is conservative and satisfies a discrete...
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