On the adaptive coupling of FEM and BEM in 2–d–elasticity

Summary. This paper concerns the combination of the finite element method (FEM) and the boundary element method (BEM) using the symmetric coupling. As a model problem in two dimensions we consider the Hencky material (a certain nonlinear elastic material) in a bounded domain with Navier–Lamé differential equation in the unbounded complementary domain. Using some boundary integral operators the problem is rewritten such that the Galerkin procedure leads to a FEM/BEM coupling and quasi–optimally convergent discrete solutions. Beside this a priori information we derive an a posteriori error estimate which allows (up to a constant factor) the error control in the energy norm. Since information about the singularities of the solution is not available a priori in many situation and having in mind the goal of an automatic mesh–refinement we state adaptive algorithms for the –version of the FEM/BEM–coupling. Illustrating numerical results are included. Received April 15, 1994 / Revised version received January 8, 1996     

Systematic study of parameters influencing the action of Rose Bengal with visible light on bacterial cells: comparison between the biological effect and singlet-oxygen production

As part of a project to study different methods for the disinfection of effluent water, the inactivation of different microorganisms (Escherichia coli, Deinococcus radiodurans and spores of Bacillus subtilis) using a combination of a photosensitizer (Rose Bengal) with simulated sunlight and oxygen was determined under various environmental conditions (temperature, pH index). In parallel, the singlet-oxygen (1O2) production was also measured under the same conditions. Whereas the vegetative cells could be inactivated much more efficiently at increased temperature and altered index of pH, the production of 1O2 remained essentially the same under these alterations. Additionally, the relations among the sensitivities of different cell types to be killed by our photodynamic treatments (PDT) were opposite to those found after exposure to ionizing radiation. The results of photodynamic experiments do not reflect the cells' capacity to repair DNA strand breaks. Spores of B. subtilis, as a nonvegetative system, could not be inactivated by illuminations up to 100 J cm-2. Together, these findings indicate that DNA is not the primary target, the inactivation of which leads to the killing of our test organisms. Instead, the cellular envelope appears to be the component being assaulted by our PDT.     

Remarks around 50 lines of Matlab: short finite element implementation

A short Matlab implementation for P ₁-x ₁ finite elements on triangles and parallelograms is provided for the numerical solution of elliptic problems with mixed boundary conditions on unstructured grids. According to the shortness of the program and the given documentation, any adaptation from simple model examples to more complex problems can easily be performed. Numerical examples prove the flexibility of the Matlab tool. This revised version was published online in June 2006 with corrections to the Cover Date.     

Coupling of mixed finite elements and boundary elements

The symmetric coupling of mixed finite element and boundaryelement methods is analysed for a model interface problem withthe Laplacian. The coupling involves a further continuous ansatzfunction on the interface to link the discontinuous displacementfield to the necessarily continuous boundary ansatz function.Quasi-optimal a priori error estimates and sharp a posteriorierror estimates are established which justify adaptive mesh-refiningalgorithms. Numerical experiments prove the adaptive couplingas an efficient tool for the numerical treatment of transmissionproblems.