We prove a convergence result for a shock-capturing streamline diffusion finite element method applied to a time-dependent scalar nonlinear hyperbolic conservation law in two space dimensions. The proof is based on a uniqueness result for measure-valued solutions by DiPerna. We also prove an almost optimal error estimate for a linearized conservation law having a smooth exact solution.

In this article, we analyze the fractional-step θ method for the time-dependent convectiondiffusion equation. In our implementation, we completely separate the convection operator from the diffusion operator, and stabilize the convective solve using a streamline upwinded PetrovGalerkin (SUPG) method. We establish a priori error estimates and show that optimal values of θ yield a scheme that is ...

Diffusion tensor magnetic resonance imaging (DT-MRI) is the first noninvasive in vivo imaging modality with the potential to generate fiber tract trajectories in soft fibrous tissues, such as the brain white matter. Several newly developed fiber reconstruction and tractography techniques based on DT-MRI are reviewed in this article, including streamline fiber tracking techniques, diffusion tens...

Abstract. In this paper, we present a shock capturing discontinuous Galerkin (SC-DG) method for nonlinear systems of conservation laws in several space dimensions and analyze its stability and convergence. The scheme is realized as a space-time formulation in terms of entropy variables using an entropy stable numerical flux. While being similar to the method proposed in [14], our approach is ne...

The paper presents a convergence analysis of a multigrid solver for a system of linear algebraic equations resulting from the discretization of a convection-diffusion problem using a finite element method. We consider piecewise linear finite elements in combination with a streamline diffusion stabilization. We analyze a multigrid method that is based on canonical intergrid transfer operators, a...

The paper presents a convergence analysis of a multigrid solver for a system of linear algebraic equations resulting from the disretization of a convection-diffusion problem using a finite element method. We consider piecewise linear finite elements in combination with a streamline diffusion stabilization . We analyze a multigrid method that is based on canonical inter-grid transfer operators, ...

Isogeometric Analysis (IGA), in combination with the Streamline Upwind Petrov– Galerkin (SUPG) stabilization, is studied for the discretization of steady-state convection-diffusion equations. Numerical results obtained for the Hemker problem are compared with results computed with the SUPG finite element method of the same order. Using an appropriate parameterization for IGA, the computed solut...

We present in this paper a thorough investigation of three-dimensional flow in a cubical cavity, subject to a constant velocity lid on its roof. In this steady-state analysis, we adopt the mixed formulation on triquadratic elements to preserve mass conservation. To resolve difficulties in the asymmetric and indefinite large-size matrix equations, we apply the BiCGSTAB solution solver. To achiev...

Local maximum entropy (LME) meshfree basis functions are among the few approximants that possess Kronecker delta property on boundary, which enable to impose essential boundary conditions directly like FEM. This study presents potential of a method based LME approximation for Convection–Diffusion problem via well-celebrated SUPG. The present Streamline Upwind Petrov–Galerkin (SUPGM) benefits fr...