In this work, we propose a new method called Petrov–Galerkin multiscale hybrid-mixed (PGMHM for short) as variant of the (MHM) method. Its construction starts from formulation Lagrange multiplier space, defined by enriching trial spaces with residual-based functions on partition faces. As result, jump terms are added to original MHM method, which penalizes lack conformity numerical solutions. c...

We present a stabilized finite element method for the scalar advection-diffusion equation, which does not require tunable mesh-dependent parameters. Stabilization is achieved by using diffusive fluxes extracted from an edge element lifting of Scharfetter-Gummel edge fluxes into the elements. Although the method is formally first-order accurate, qualitative numerical studies suggest that it occu...

A new dual-Petrov-Galerkin method is proposed, analyzed and implemented for third and higher odd-order equations using a spectral discretization. The key idea is to use trial functions satisfying the underlying boundary conditions of the differential equations and test functions satisfying the “dual” boundary conditions. The method leads to linear systems which are sparse for problems with cons...

A new adaptive finite element method for convection-dominated problems is presented. A special feature of the method is that it is based on a Petrov-Galerkin scheme for spatial approximation at a typical time-step which employs test functions chosen so that the approximate solution coincides with the exact solution at the nodes of finite element grid. This procedure makes possible the derivatio...

A method for model reduction of dynamical systems with the second order structure is proposed in this paper. The proposed technique preserves the second order structure of the system, and also preserves the stability of the original systems. The method uses the controllability and observability gramians within the time interval to build the appropriate Petrov-Galerkin projection for dynamical s...

using the highly recommended numerical techniques, a finite element computer code is developed to analyse the steady incompressible, laminar and turbulent flows in 2-d domains with complex geometry. the petrov-galerkin finite element formulation is adopted to avoid numerical oscillations. turbulence is modeled using the two equation k-ω model. the discretized equations are written in the form o...