Solving Minimal Residual Methods in \(W^{-1,p'}\) with Large Exponents p

We introduce a numerical scheme that approximates solutions to linear PDE’s by minimizing a residual in the \(W^{-1,p'}(\Omega )\) $W^{-1,p^{\prime }}(\mathrm{\Omega })$ 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.