Current research is concerned with problems from Numerical Analysis, Applied Mathematics, and Scientific Computing. We are particularly interested in developing and analysing new discretisation methods for the numerical solution of partial differential equations.
Recent projects comprise:
- The development of new high-order discretisation spaces based upon radial basis functions and scattered data. These are flexible tools particularly for problems with moving boundaries or in higher dimensional spaces.
- The investigation of efficient solvers for fluid-structure-interaction problems as they typically appear in aeroelasticity.
- The development of divergence-free approximation spaces with applications to fluid-flow problems.
- The analysis of multiscale phenomena using scaled versions of compactly supported radial basis functions.
- The application of meshfree methods to dynamical systems with applications in biomechanics.
- The development of meshfree approximation methods on the sphere with applications to geo-science problems and weather modelling.
- The application of meshfree methods to semilinear parabolic problems on (evolving) surfaces.
More details about this can be found by consulting the list of publications and will, hopefully, also follow on this page. Older research was concerned with surface reconstruction from unorganised, three dimensional point clouds. Details can be found following:
To our projects