Abstract
AbstractWe introduce a numerical scheme that approximates solutions to linear PDE’s by minimizing a residual in the $$W^{-1,p'}(\Omega )$$
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 $$p\gg 2$$
p
≫
2
. Such large exponents remedy instabilities of finite element methods for problems like convection-dominated diffusion.
Funder
Deutsche Forschungsgemeinschaft
Universität Leipzig
Publisher
Springer Science and Business Media LLC