We compare numerically the performance of a new continuous-discontinuous finite element method (CDFEM) for linear convection-diffusion equations with three well-known upwind finite element formulations, namely with the streamline upwind Petrov-Galerkin finite element method, the residualfree bubble method and the discontinuous Galerkin finite element method. The defining feature of the CDFEM is...

We present a method for the stylization of mountainous terrains that allows creating abstract representations in different rendering styles. Our method consists of two major components: structure-aware terrain filtering and streamline-based hatching. For a given input terrain we compute different Levels-of-Detail (LoD) according to a crest line oriented importance measure and then filter each L...

A finite element based level set method is proposed for structural topology optimization. Because both the level set equation and the reinitialization equation are advection dominated partial differential equations, the standard Galerkin finite element method may produce oscillating results. In this paper, both equations are solved using a streamline diffusion finite element method (SDFEM). The...

‎let $m^n$ be an $n(ngeq 3)$-dimensional complete connected and‎ ‎oriented spacelike hypersurface in a de sitter space or an anti-de‎ ‎sitter space‎, ‎$s$ and $k$ be the squared norm of the second‎ ‎fundamental form and gauss-kronecker curvature of $m^n$‎. ‎if $s$ or‎ ‎$k$ is constant‎, ‎nonzero and $m^n$ has two distinct principal‎ ‎curvatures one of which is simple‎, ‎we obtain some‎ ‎charact...

In this work we consider the design of robust and eecient nite element approximation methods for solving advection-diiusion equations. Speciically, we consider the stabilisation of discrete approximations using uniform grids which do not resolve boundary layers, as might arise using a multi-level (or multigrid) iteration strategy to solve the discrete problem. Our analysis shows that when using...

many large oil and gas fields in the most productive world regions happen to be fractured. the exploration and development of these reservoirs is a true challenge for many operators. these difficulties are due to uncertainties in geological fracture properties such as aperture, length, connectivity and intensity distribution. to successfully address these challenges, it is paramount to improve ...

We analyse nite element approximations of a stationary convection-diiusion problem. We prove global and localised a posteriori error estimates in the maximum norm. For the discretisation we use the Streamline Diiusion method.