A mesh-free method based on moving least squares approximation (MLS)  and weak form of governing equations including two dimensional equations of motion and Maxwell’s equation is used to analyze the free vibration of functionally graded piezoelectric material (FGPM) beams. Material properties in beam are determined using a power law distribution. Essential boundary conditions are imposed by the...

in this paper, a positive definite semi-discrete mixed finite element method was presented for two-dimensional parabolic equations. in the new positive definite systems, the gradient equation and flux equations were separated from their scalar unknown equations.  also, the existence and uniqueness of the semi-discrete mixed finite element solutions were proven. error estimates were also obtaine...

We analyse a Eulerian Finite Element method, combining time-stepping scheme applied to the time-dependent Stokes equations using CutFEM approach with inf-sup stable Taylor-Hood elements for spatial discretisation. This is based on method introduced by Lehrenfeld \& Olshanskii [ESAIM: M2AN 53(2):585--614] in context of scalar convection-diffusion problems moving domains, and extended non-station...

<p style='text-indent:20px;'>In this article, we develop a new mixed immersed finite element discretization for two-dimensional unsteady Stokes interface problems with unfitted meshes. The proposed IFE spaces use conforming linear elements one velocity component and non-conforming the other component. pressure is approximated by piecewise constant. Unisolvency, among fundamental propertie...