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.

unlike the classical deformation analysis of the earth crust, which derives the planar and vertical strains separately, in this study, we have offered a method for 3-d deformation study based on intrinsic geometry of the manifolds on the topographic surface of the earth. in this way, our method would be based on the 2-d metric tensor of horizontal deformation and 2-d curvature tensor of vertica...

In this paper we prove a posteriori L2(L2) and L∞(H−1) residual based error estimates for a finite element method for the one-dimensional time dependent coupling equations of two scalar conservation laws. The underlying discretization scheme is Characteristic Galerkin method which is the particular variant of the Streamline diffusion finite element method for δ = 0. Our estimate contains certai...

Numerical investigation of mixed convection flow in a concentration-stratified fluid-saturated vertical square porous enclosure is investigated by Galerkin finite element method. The forced flow conditions are imposed by providing an inlet at the bottom wall and an outlet with a suction on the top wall. The free convection is induced by introducing a hot but isothermal temperature on the left v...

In this work we compare semi-discrete formulations to obtain numerical solutions for the 1D Burgers equation. The formulations consist in the discretization of the time-domain via multi-stage methods of second and fourth order: R11 and R22 Padé approximants, and of the spatial-domain via finite element methods: least-squares (MEFMQ), Galerkin (MEFG) and Streamline-Upwind Petrov-Galerkin (SUPG)....

Using the visual search method, we show that stimuli that contain curvature discontinuities (i.e., points where the second derivative along an image contour is not defined) are easily found among stimuli containing only smooth changes in curvature. Curved stimuli that lack curvature discontinuities, however, are difficult to find among distractors that have them. These results suggest that the ...

We present a stabilized finite element method for the scalar advection-diffusion equation, which does not require tunable mesh-dependent parameters. Stabilization is achieved by using diffusive fluxes extracted from an edge element lifting of Scharfetter-Gummel edge fluxes into the elements. Although the method is formally first-order accurate, qualitative numerical studies suggest that it occu...

We discuss the behavior of the minimal residual method applied to stabilized discretizations of oneand two-dimensional model problems for the stationary convection-diffusion equation. In the one-dimensional case, it is shown that eigenvalue information for estimating the convergence rate of the minimal residual method is highly misleading due to the strong nonnormality of these operators for la...