PUB - Publikationen an der Universität Bielefeld

We introduce a numerical scheme that approximates solutions to linear PDE’s by minimizing a residual in the $$W^{-1,p'}(\Omega )$$ $W^{-1,p^{\prime }}\left(\Omega \right)$ norm with exponents $$p> 2$$ $p>2$ . The resulting problem is solved by regularized Kačanov iterations, allowing to compute the solution to the non-linear minimization problem even for large exponents $$p\gg 2$$ $p\gg 2$ . Such large exponents remedy instabilities of finite element methods for problems like convection-dominated diffusion.