We present in this paper a new a posteriori error estimator for the Baumann-Oden version of the Discontinuous Galerkin Method. The error estimator is based on the residual of the partial differential equation. In the case of the reaction-diffusion equation, the norm of the residual is shown to be equivalent to the error in some specific energy-type norms. We propose here a method to efficiently...

In the present study the problem of mixed convection flow in the presence of magnetic field in a lid-driven square cavity with internal heat generation or absorption and uniform heating of bottom wall were investigated numerically. The square cavity vertical walls are maintained at cold temperature while the upper wall is insulated. The physical problem is then expressed mathematically by a set...

A numerical study of the unsteady mixed convection heat transfer characteristics of an Ag–water nanofluid confined within a square shape lid-driven cavity has been carried out. The Galerkin weighted residual of the finite element method has been employed to investigate the effects of the periodicity of sinusoidal boundary condition for a wide range of Grashof numbers (Gr) (105 to 107) with the ...

Water diffusion within the brain is studied numerically for various clinical conditions. The numerical procedure used in this work is based on the Galerkin weighted residual method of finite-element formulation. A wide range of pertinent parameters such as Lewis number, cell volume, and the buoyancy ratio are considered in the present study. Comparisons with previously published work show excel...

Galerkin and weighted Galerkin methods are proposed for the numerical solution of parabolic partial differential equations where the diffusion coefficient takes different signs. The approach is based on a simultaneous discretization of space and time variables by using continuous finite element methods. Under some simple assumptions, error estimates and some numerical results for both Galerkin ...

In the present work, axial static analysis of nanorods under triangular loading is presented via Eringen’s nonlocal differential model. Three weighted residual methods (Subdomain, Galerkin and Least squares methods) are used to obtain exact deflection. These require that integral error with different assumptions over domain be set zero. The number equations have equal unknown terms. A cubic dis...

This paper presents a primal interface formulation that is derived in a systematic manner from a Lagrange multiplier method to provide a consistent framework to couple different partial differential equations (PDE) as well as to tie together nonconforming meshes. The derivation relies crucially on concepts from the Variational Multiscale (VMS) approach wherein an additive multiscale decompositi...

Abstract Due to simplicity in implementation and data structure, elements with equal‐order interpolation of velocity pressure are very popular finite‐element‐based flow simulations. Although such pairs inf‐sup unstable, various stabilization techniques exist circumvent that yield accurate approximations. The most one is the pressure‐stabilized Petrov–Galerkin (PSPG) method, which consists relax...

This work focuses on the dynamical behavior of carbon nanotubes, including vibration, wave propagation and fluid-structure interaction. In the present research, transverse vibration of nano fluid conveying carbon nanotubes is investigated. To this end, based on the nonlocal and strain-inertia gradient continuum elasticity theories and by using rod and Euler-Bernoulli beam models, the system’s d...