This paper describes the use of a quadratic manifold for the model order reduction of structural dynamics problems featuring geometric nonlinearities. The manifold is tangent to a subspace spanned by the most relevant vibration modes, and its curvature is provided by modal derivatives obtained by sensitivity analysis of the eigenvalue problem, or its static approximation, along the vibration mo...

In this paper we show that mixed nite element methods for a fairly general second order elliptic problem with variable coeecients can be given a non-mixed formulation. (Lower order terms are treated, so our results apply also to parabolic equations.) We deene an approximation method by incorporating some projection operators within a standard Galerkin method, which we call a projection nite ele...

In this paper, we introduce novel discontinuous Galerkin (DG) schemes for the Cahn-Hilliard equation, which arises in many applications. The method is designed by integrating mixed DG spatial discretization with \emph{Invariant Energy Quadratization} (IEQ) approach time discretization. Coupled a projection, resulting IEQ-DG are shown to be unconditionally energy dissipative, and can efficiently...

In this paper we show that mixed nite element methods for a fairly general second order elliptic problem with variable coeecients can be given a non-mixed formulation. (Lower order terms are treated, so our results apply also to parabolic equations.) We deene an approximation method by incorporating some projection operators within a standard Galerkin method, which we call a projection nite ele...

In this paper we describe a second-order projection method for the time-dependent, incompressible Navier-Stokes equations. As in the original projection method developed by Chorin, we first solve diffusion-convection equations to predict intermediate velocities which are then projected onto the space of divergence-free vector fields. By introducing more coupling between the diffusion--{;onvecti...

The present work considers a stochastic segmentation method on images in the presence of noise within PDE-based image processing framework. Classical methods are not able to capture error propagation uncertain estimated input data and their impact final result, which can be great importance for clinical decisions. Therefore, an intrusive generalized polynomial chaos (gPC) expansion level-set ba...

In this paper we show that mixed finite element methods for a fairly general second-order elliptic problem with variable coefficients can be given a nonmixed formulation. (Lower-order terms are treated, so our results apply also to parabolic equations.) We define an approximation method by incorporating some projection operators within a standard Galerkin method, which we call a projection fini...

An efficient and accurate numerical scheme is presented for the axisymmetric Navier–Stokes equations in primitive variables in a cylinder. The scheme is based on a new spectral-Galerkin approximation for the space variables and a secondorder projection scheme for the time variable. The new spectral-projection scheme is implemented to simulate the unsteady incompressible axisymmetric flow with a...

Abstract In this paper, we study the error estimates of local discontinuous Galerkin methods based on generalized numerical fluxes for one-dimensional linear fifth order partial differential equations. We use a newly developed global Gauss–Radau projection to obtain type optimal estimates. The experiments show that scheme coupled with third implicit Runge–Kutta method can achieve $(k+1)$ <mml:m...

We examine some differential geometric approaches to finding approximate solutions to the continuous time nonlinear filtering problem. Our primary focus is a new projection method for the optimal filter infinite dimensional Stochastic Partial Differential Equation (SPDE), based on the direct L2 metric and on a family of normal mixtures. We compare this method to earlier projection methods based...