A posteriori error estimates and adaptive methods for convection dominated transport processes

In this thesis we derive robust a posteriori error estimates <br>for finite volume approximations of convection dominated nonlinear <br>transport problems. <br>Robustness means that the error estimates are uniform with respect to <br>vanishing diffusion coefficients. <br>The a posteriori error estimates give upper bounds for the error in the <br>L^1 norm between the exact solution and the approximate solution. <br>Hereby, the upper bounds only depend on computable constants and the <br>approximate solution itself. Therefore, the upper bound can be computed. <br>Using these theoretical results adaptive solution strategies are deduced, <br>implemented and tested for some model problems. <br>These adaptive techniques are applicable e.g. in two phase flow problems in <br>porous media or in the simulation of subsurface contaminant transport processes. <br>For two phase flow and density driven flow in porous media the applicability <br>is shown in several examples.

Author dc:creator

• Ohlberger, Mario

Contributors dc:contributor

• Kröner, Dietmar

• A posteriori Fehlerabschätzungen, adaptive Verfahren
• konvektionsdominante Probleme,
• A posteriori error estimates
• adaptive methods
• finite volume
• convection dominated
• unstructured grids

Repository record source_url

https://freidok.uni-freiburg.de/data/178

OAI identifier oai:identifier

oai:freidok.uni-freiburg.de:178