English

Solving Minimal Residual Methods in $W^{-1,p'}$ with large Exponents $p$

Numerical Analysis 2023-12-11 v2 Numerical Analysis

Abstract

We introduce a numerical scheme that approximates solutions to linear PDE's by minimizing a residual in the W1,p(Ω)W^{-1,p'}(\Omega) norm with exponents p>2p> 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 p2p\gg 2. Such large exponents remedy instabilities of finite element methods for problems like convection-dominated diffusion.

Keywords

Cite

@article{arxiv.2307.05178,
  title  = {Solving Minimal Residual Methods in $W^{-1,p'}$ with large Exponents $p$},
  author = {Johannes Storn},
  journal= {arXiv preprint arXiv:2307.05178},
  year   = {2023}
}
R2 v1 2026-06-28T11:26:59.130Z