Towards Robust Adaptive Methods for Singularly Perturbed Problems

• Applicant: Professor Dr. Rüdiger Verfürth
• Subject Area: Mathematics
• Term: from 2014 to 2017
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 260814742

Adaptive discretization methods are an indispensable tool for the efficient solution of problems in technics and natural sciences. The goal is to obtain a (nearly) optimal balance of cost to accuracy of the discrete solution. The development of of such methods is linked to a posteriori error estimation and adaptive approximation. Many practical problems are modeled by families of partial differential equations that contain parameters and which give rise to singularly perturbed problems. The balance of cost to accuracy should then be robust in the sense that it holds uniformly in the whole range of parameters. The proposed project aims at developing robust adaptive methods for such singularly perturbed problems. Starting from recent results of Tantardini, Veeser und Verfürth (submitted 2013) for singularly perturbed reaction-diffusion problems we intend to investigate in particular singularly perturbed convection-diffusion equations and problems with large jumps in the diffusivity.

• DFG Programme: Research Grants
• International Connection: Italy
• Participating Person: Professor Dr. Andreas Veeser