Solving Minimal Residual Methods in W^-1,p with large Exponents p

07/11/2023

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by   Johannes Storn, et al.

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We introduce a numerical scheme that approximates solutions to linear PDE's by minimizing a residual in the W^-1,p(Ω) 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≫ 2. Such large exponents remedy instabilities of finite element methods for problems like convection-dominated diffusion.