We present a Petrov-Gelerkin (PG) method for class of nonlocal convection-dominated diffusion problems. There are two main ingredients in our approach. First, we define the norm on test space as induced by trial norm, i.e., optimal so that inf-sup condition can be satisfied uniformly independent problem. show well-posedness problems under with general assumptions and convection kernels. Second,...

We use two meshless local Petrov-Galerkin formulations, namely, the MLPG1 and the MLPG5, to analyze infinitesimal deformations of a homogeneous and isotropic thick elastic plate with a higher-order shear and normal deformable plate theory. It is found that the two MLPG formulations give results very close to those obtained by other researchers and also by the threedimensional analysis of the pr...

The standard in rod finite element formulations is the Bubnov–Galerkin projection method, where test functions arise from a consistent variation of ansatz functions. This approach becomes increasingly complex when highly nonlinear are chosen to approximate rod's centerline and cross-section orientations. Using Petrov–Galerkin we propose whole family nodal generalized virtual displacements veloc...

We develop and analyze an ultraweak formulation of linear PDEs in nondivergence form where the coefficients satisfy Cordes condition. Based on we propose discontinuous Petrov–Galerkin (DPG) methods. investigate Fortin operators for fully discrete schemes provide a posteriori estimators methods under consideration. Numerical experiments are presented case uniform adaptive mesh-refinement.

The present investigation analyses the critical buckling studies of triple-walled carbon nanotube using Euler─Bernoulli model. study deals with three different boundary conditions, namely, simply-simply, clamped-clamped, and clamped-simply supported nanotube. Using Bubnov─Galerkin Petrov─Galerkin methods, continuum model estimates load. main advantage these two approximate methods is to obtain ...