This paper is devoted to the analysis of the discontinuous Galerkin finite element method (DGFEM) applied to the space semidiscretization of a nonlinear nonstationary convection-diffusion Dirichlet problem. General nonconforming simplicial meshes are considered and the SIPG scheme is used. Under the assumption that the exact solution is sufficiently regular an L∞(L2)-optimal error estimate is d...

This article considers transient, planar Poiseuille flows for viscoelastic fluids. We propose a novel time-dependent hybrid finite volume (fv)/finite element (fe) algorithm. This approach combines a Taylor-Galerkin fe-treatment for mass and momentum conservation equations, with a cell-vertex fv-discretisation of the hyperbolic stress constitutive equation. A consistent formulation for the const...

We have successfully extended our implicit hybrid finite element/volume solver to flows involving two immiscible fluids. The solver is based on the segregated pressure correction or projection method on staggered unstructured hybrid meshes. An intermediate velocity field is first obtained by solving the momentum equations with the matrix-free implicit cell-centered finite volume method. The pre...

I n recent years, many numerical methods have been proposed for solving fuzzy linear integral equations. For example, in [10], the authors used the divided differences and finite differences methods for solving a parametric of the fuzzy Fredholm integral equations of the second kind. Also, in [9], a numerical method is proposed for the approximate solution of fuzzy linear Fredholm functional in...

methods are two classes of high order, high resolution methods suitable for convection dominated simulations with possible discontinuous or sharp gradient solutions. In [18], we first review these two classes of methods, pointing out their similarities and differences in algorithm formulation, theoretical properties, implementation issues, applicability, and relative advantages. We then present...

A novel high-order method, termed flux correction, previously formulated for inviscid flows, is extended to viscous flows on arbitrary triangular grids. The correction method involves the addition of truncation errorcanceling terms to the second-order linear Galerkin (node-centered finite volume) scheme to produce a thirdorder inviscid and fourth-order viscous scheme. The correction requires mi...

We present a new numerical method, based on a coupling of finite elements and boundary elements, to solve a fluid–solid interaction problem posed in the plane. The boundary unknowns involved in our formulation are approximated by a spectral method. We provide error estimates for the Galerkin method, propose fully discrete schemes based on elementary quadrature formulas and show that the perturb...