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'(Ω ) W - 1 , p ′ ( Ω ) 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 2 p ≫ 2 . Such large exponents remedy instabilities of finite element methods for problems like convection-dominated diffusion.