abstract This paper is devoted to the study of a posteriori error estimates and adaptive methods for a mixed nite element-nite volume approximation for single and two phase ow problems in porous media. In a rst step we analyze a scalar nonlinear convection diiusion equation and give a rigorous a posteriori error estimate for the Cauchy problem. In a second step these results are used to impleme...

We prove pointwise a posteriori error estimates for semiand fullydiscrete finite element methods for approximating the solution u to a parabolic model problem. Our estimates may be used to bound the finite element error ‖u−uh‖L∞(D), where D is an arbitrary subset of the space-time domain of definition of the given PDE. In contrast to standard global error estimates, these estimators de-emphasiz...

Multiresolution meshes provide an efficient and structured representation of geometric objects. To increase the mesh resolution only at vital parts of the object, adaptive refinement is widely used. We propose a lossless compression scheme for these adaptive structures that exploits the parent-child relationships inherent to the mesh hierarchy. We use the rules that correspond to the adaptive r...

Mesh refinement procedures for the solution of three dimensional problems are described. The computational domain is represented by an assembly of tetrahedral elements and the mesh refinement is acheived by the bisection and Rivara methods using an explicit mesh density function coupled with an automatic 3D mesh generator. A couple of benchmark examples is used to compare the performance of bot...

During a numeric simulation based on the finite element method, the h-refinement of the mesh consists in splitting the elements where an error indicator is higher than a threshold. One major point is that the final mesh must be conformal. When the mesh is defined only by triangles or tetrahedra, the junction between two zones with a different level of refinement has been solved for many years. ...

The Zienkiewicz—Zhu error estimate is slightly modified for the hierarchical p-refinement, and is then applied to three plane elastostatic problems to demonstrate its effectiveness. In each case, the error decreases rapidly with an increase in the number of degrees of freedom. Thus Zienkiewicz—Zhu’s error estimate can be used in the hp-refinement of finite element meshes. ( 1999 Elsevier Scienc...

High resolution models of air pollution transport and transformation are necessary in order to test possible abatement strategies based on pollution control and to forecast high pollution episodes. Models are especially relevant for secondary pollutants like ozone and nitrogen dioxide which are formed in the atmosphere through nonlinear chemical reactions involving primary pollutant species far...

We propose an anisotropic refinement strategy which is specially designed for the efficient numerical resolution of internal and boundary layers. This strategy is based on the directed refinement of single triangles together with adaptive multilevel grid orientation. Compared to usual methods, the new anisotropic refinement ends up in more stable and more accurate solutions at much less computa...

Adaptivity is a key tool for HPC, the larger the problem becomes, the more important adaptive grid resolution becomes. This can be seen from the following example computed by Arne Nägel, Sebastian Reiter and Andreas Vogel. Take the skin permeation model from (Kreienbühl et al, this issue) and do a weak scaling of this problem with uniform refinement up to 65,536 cores (JuQueen) and compare with...

We propose a new moving mesh method suitable for solving timedependent partial differential equations (PDEs) in R which have fine scale solution structures that develop or dissipate. A key feature of the method is its ability to add or remove mesh nodes in a smooth manner and that it is consistent with r-refinement schemes. Central to our approach is an implicit representation of a Lagrangian m...