Generic implementation of finite element methods in the Distributed and Unified Numerics Environment (DUNE)

summary:In this paper we describe PDELab, an extensible C++ template library for finite element methods based on the Distributed and Unified Numerics Environment (Dune). PDELab considerably simplifies the implementation of discretization schemes for systems of partial differential equations by setting up global functions and operators from a simple element-local description. A general concept for incorporation of constraints eases the implementation of essential boundary conditions, hanging nodes and varying polynomial degree. The underlying Dune software framework provides parallelization and dimension-independence

Modeling and Simulation of Hairy Root Growth

A multiscale approach is presented to model growth of hairy roots. On the macroscopic scale, a continuous model is derived, which includes growth and nutrient transport. Water transport is considered on the microscopic scale. A Discontinuous Galerkin scheme for complex geometries is used to compute the permeability of root bulks. This permeability constitutes the linkage between microand macroscopic scale. The models are applied then to describe shaker cultures of hairy roots and simulations are compared to measurements