In this thesis we are interested in a particular class of problems which frequently appear in robotics (and many other areas as chemistry, molecular biology, Computer-Aided Design (CAD), and aeronautics). They are systems of distance equations with uncertainties. Uncertain values mean values which are not exactly determined but are bounded by well-known limits. These values are represented as i...

The presented article contains a 3D mesh generation routine optimized with the Metropolis algorithm. The procedure enables to produce meshes of a prescribed volume V0 of elements. The finite volume meshes are used with the Finite Element approach. The FEM analysis enables to deal with a set of coupled nonlinear differential equations that describes the electrodiffusional problem. Mesh quality a...

Recently ([21]), a new meshfree approximation method for Darcy’s problem has been introduced and analyzed. This method is based on a symmetric collocation approach using radial basis functions producing solutions with an analytically divergence-free velocity part. However, the error analysis provided in [21] works only for smooth solutions, where the smoothness is intrinsically linked to the sm...

Several approximation algorithms with proven performance guarantees have been proposed to find approximate solutions to classical combinatorial optimization problems. However, theoretical results may not reflect the experimental performance of the proposed algorithms. As a consequence, a question arises: how “far” from the theoretically proved performance are the experimental results?We conduct...

The main aim of randomized search heuristics is to produce good approximations of optimal solutions within a small amount of time. In contrast to numerous experimental results, there are only a few theoretical results on this subject. We consider the approximation ability of randomized search for the class of covering problems and compare single-objective and multi-objective models for such pro...

Standard weak solutions to the Poisson problem on a bounded domain have squareintegrable derivatives, which limits the admissible regularity of inhomogeneous data. The concept of solution may be further weakened in order to define solutions when data is rough, such as for inhomogeneous Dirichlet data that is only square-integrable over the boundary. Such very weak solutions satisfy a nonstandar...