Numerical Methods for the PDES on Curves and Surfaces
Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
Curves and surfaces are manifolds that can be represented using implicit and parametric methods. With a representation in hand, one can define a partial differential equation on the manifold using differential tangential calculus. The solution of these PDEs is quite interesting because they have many applications in a variety of areas including fluid dynamics, solid mechanics, biology and image processing.In this thesis, we examine two numerical methods for the solution of PDEs on manifolds: a so called cut finite element method and isogeometric analysis. We review the theoretical framework of the two methods and implement them to solve example problems in two and three dimensions: the Laplace-Beltrami problem, the Laplace-Beltrami eigenvalue problem, the biharmonic problem and the time-dependent advection diffusion problem. We compare the methods and we confirm that the numerical results agree with the exact solutions and that they obey the theoretical a priori error estimates.
Place, publisher, year, edition, pages
, UMNAD, 971
Engineering and Technology
IdentifiersURN: urn:nbn:se:umu:diva-81124OAI: oai:DiVA.org:umu-81124DiVA: diva2:652933
Master's Programme in Computational Science and Engineering