This paper presents mechanical behavior of a functionally graded (FG) cantilever micro-beam subjected to a nonlinear electrostatic pressure and thermal moment considering effects of material length scale parameters. Material properties through the beam thickness direction are graded. The top surface of the micro-beam is made of pure metal and the bottom surface from a mixture of metal and ceram...

We numerically solve parabolic problems in , , where is a bounded interval and is a strongly elliptic integrodifferential operator of order ! #" %$'& . A discontinuous Galerkin (dG) discretization in time and a wavelet discretization in space are used. The densely populated matrices in the corresponding linear systems of equations are replaced by sparse ones using appropriate wavelet compressio...

In this paper we analyze local properties of the Continuous Interior Penalty (CIP) Method for a model convection-dominated singularly perturbed convection-diffusion problem. We show weighted a priori error estimates, where the weight function exponentially decays outside the subdomain of interest. This result shows that locally, the CIP method is comparable to the Streamline Diffusion (SD) or t...

In this paper we establish a best approximation property of fully discrete Galerkin finite element solutions of second order parabolic problems on convex polygonal and polyhedral domains in the L∞ norm. The discretization method uses of continuous Lagrange finite elements in space and discontinuous Galerkin methods in time of an arbitrary order. The method of proof differs from the established ...

Size-dependent vibrational and instability behavior of fluid-conveying magneto-electro-elastic (MEE) tubular nano-beam subjected to magneto-electric potential and thermal field has been analyzed in this study. Considering the fluid-conveying nanotube as an Euler-Bernoulli beam, fluid-structure interaction (FSI) equations are derived by using non-classical constitutive relations for MEE material...

The global Galerkin or weighted residuals method applied to the incompressible Navier–Stokes equations is considered. The basis functions are assumed to be divergence-free and satisfy all the boundary conditions. The method is formulated for an arbitrary inner product, so that the pressure cannot be eliminated by Galerkin projections on a divergence-free basis. A proposed straightforward proced...

We propose a general framework for approximating the potential of mean force (PMF) along a reaction coordinate in conformational space. This framework, based on the method of weighted residuals, can be viewed as a generalization of thermodynamic integration and direct histogram methods. Using weighted residuals allows for higher-order approximations to the PMF in the form of a global spectral m...

We apply polynomial approximation methods—known in the numerical PDEs context as spectral methods—to approximate the vector-valued function that satisfies a linear system of equations where the matrix and the right-hand side depend on a parameter. We derive both an interpolatory pseudospectral method and a residual-minimizing Galerkin method, and we show how each can be interpreted as solving a...