In this article, we propose and analyze the robust modified characteristics variational
multiscale (MCVMS) method for solving the blood solute dynamics model, which consists of …

In this paper, we consider a heterogeneous model of solute absorption processes by the
arterial wall. This model is based on an advection-diffusion equation describing the solute …

Computational cardiovascular flow analysis can provide valuable information to medical
doctors in a wide range of patientspecific cases, including cerebral aneurysms, aortas and …

This paper presents a variational multiscale (VMS) based finite element method where the
stabilization parameter is computed dynamically. The current dynamic procedure takes in a …

In this paper, a modified method of characteristics variational multiscale (MMOCVMS) finite
element method is presented for the time dependent Navier-Stokes problems, which is …

In this paper, the characteristic variational multiscale (C-VMS) method is proposed for
solving two-dimensional (2D) convection-dominated convection–diffusion–reaction …

We analyze the application of the residual-based variational multiscale (VMS) method to the
solution of a generic partial differential equation. We prove that the model terms introduced …

In this paper, the convergence of a general algorithm with θ-type stabilization form for the
variational multiscale (VMS) method is presented. Meanwhile, explicit-type and implicit-type …

Diverse transport problems, especially those based on fluid flow models, are intrinsically
multiscale and nonlinear, characteristics that often lead to intricate dynamics such as the …

In this article, we present a finite element variational multiscale (VMS) method for
incompressible flows based on two local Gauss integrations, and compare it with common …