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

翻译：本文提出一种数值格式，通过在$W^{-1,p'}(\Omega)$范数中以指数$p>2$最小化残差来逼近线性偏微分方程的解。所得问题通过正则化Kacanov迭代求解，即使对于大指数$p\gg 2$，也能计算非线性最小化问题的解。此类大指数可补救对流主导扩散等问题中有限元方法的不稳定性。