Funding Information Russian Science Foundation, Grant/Award Number: 14-31-00024 Summary The paper studies numerical properties of LU and incomplete LU factorizations applied to the discrete linearized incompressible Navier–Stokes problem also known as the Oseen problem. A commonly used stabilized Petrov–Galerkin finite element method for the Oseen problem leads to the system of algebraic equati...

Article history: Received 9 August 2012 Received in revised form 12 December 2012 Accepted 24 January 2013 Available online 14 February 2013

We propose a linearized semi-implicit and decoupled finite element method for the incompressible Navier--Stokes equations with variable density. Our is fully discrete shown to be unconditionally stable. The velocity equation solved by an H1-conforming method, upwind discontinuous Galerkin post-processed adopted density equation. proposed proved convergent in approximating reasonably smooth solu...

Least-squares Petrov–Galerkin (LSPG) model-reduction techniques such as the Gauss–Newton with Approximated Tensors (GNAT) method have shown promise, as they have generated stable, accurate solutions for large-scale turbulent, compressible flow problems where standard Galerkin techniques have failed. However, there has been limited comparative analysis of the two approaches. This is due in part ...

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...

In this paper we will present the local stability analysis and local error estimate for the local discontinuous Galerkin (LDG)method, when solving the time-dependent singularly perturbed problems in one dimensional spacewith a stationary outflow boundary layer. Based on a general framework on the local stability, we obtain the optimal error estimate out of the local subdomain, which is nearby t...

and Applied Analysis 3 nonlinear term is treated with the Chebyshev collocation method. The time discretization is a classical Crank-Nicholson-leap-frog scheme. Yuan and Wu 43 extended the Legendre dual-Petrov-Galerkin method proposed by Shen 44 , further developed by Yuan et al. 45 to general fifth-order KdV-type equations with various nonlinear terms. The main aim of this paper is to propose ...

A convergence analysis to the weak solution is derived for interior penalty discontinuous Galerkin methods applied to the heat equation in two and three dimensions under general mixed boundary conditions. Strong convergence is established in the DG norm, as well as in the L norm, in space and in the L norm in time.