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Recently Masud and Hughes proposed a stabilized mixed finite element formulation for Darcy flow. An interesting feature of this formulation is that there are no mesh-dependent parameters. In the… (More)

- Swaroop Darbha, K. B. Nakshatrala, K. R. Rajagopal
- J. Franklin Institute
- 2010

In this paper, we consider the vibratory motions of lumped parameter systems wherein the components of the system cannot be described by constitutive expressions for the force in terms of appropriate… (More)

- K. B. Nakshatrala, K. R. Rajagopal
- ArXiv
- 2009

Abstract. Much of the work on flow through porous media, especially with regard to studies on the flow of oil, are based on “Darcy’s law” or modifications to it such as Darcy-Forchheimer or Brinkman… (More)

- D. Z. Turner, K. B. Nakshatrala, K. D. Hjelmstad
- ArXiv
- 2008

The following paper compares a consistent Newton-Raphson and fixed-point iteration based solution strategy for a variational multiscale finite element formulation for incompress-ible Navier–Stokes.… (More)

- K. B. Nakshatrala, Albert J. Valocchi
- J. Comput. Physics
- 2009

We consider the tensorial diffusion equation, and address the discrete maximum-minimum principle of mixed finite element formulations. In particular, we address non-negative solutions (which is a… (More)

We derive a numerical method for Darcy flow, hence also for Poisson’s equation in first order form, based on discrete exterior calculus (DEC). Exterior calculus is a generalization of vector calculus… (More)

- Harsha Nagarajan, K. B. Nakshatrala
- ArXiv
- 2010

Abstract. In this paper, we consider anisotropic diffusion with decay, which takes the form α(x)c(x) − div[D(x)grad[c(x)]] = f(x) with decay coefficient α(x) ≥ 0, and diffusivity coefficient D(x) to… (More)

- K. B. Nakshatrala, Harsha Nagarajan
- ArXiv
- 2012

Transient diffusion equations arise in many branches of engineering and applied sciences (e.g., heat transfer and mass transfer), and are parabolic partial differential equations. It is well-known… (More)

Abstract. Much of the work on flow through porous media, especially with regard to studies on the flow of oil, are based on “Darcy’s law” or modifications to it such as Darcy-Forchheimer or Brinkman… (More)

In this paper we present a mixed stabilized finite element formulation that does not lock and also does not exhibit unphysical oscillations near the incompressible limit. The new mixed formulation is… (More)