2024/11/23 by Marcin Łoś, Łoś, Marcin, Tomasz Służalec +5
Computer Science · Engineering · Mathematics · #35A25 #65D99 #65M60 #Advanced Numerical Analysis Techniques #FOS: Mathematics #G.1.8 #G.4 #I.6.3 #Iterative Methods for Nonlinear Equations #Numerical Analysis (math.NA) #Polynomial and algebraic computation
paper · pdf · doi:10.48550/arxiv.2411.15565
openalex publication_date 2024/11/23 · openalex created_date 2024/12/04 · openalex updated_date 2026/07/28
We compare several stabilization methods in the context of isogeometric analysis and B-spline basis functions, using an advection-dominated advection\revision-diffusion as a model problem. We derive (1) the least-squares finite element method formulation using the framework of Petrov-Galerkin method with optimal test functions in the L2 norm, which guarantee automatic preservation of the inf-sup condition of the continuous formulation. We also combine it with the standard Galerkin method to recover (2) the Galerkin/least-squares formulation, and derive coercivity constant bounds valid for B-spline basis functions. The resulting stabilization method are compared with the least-squares and (3) the Streamline-Upwind Petrov-Galerkin (SUPG)method using again the Eriksson-Johnson model problem. The results indicate that least-squares (equivalent to Petrov-Galerkin with L2-optimal test functions) outperforms the other stabilization methods for small Péclet numbers, while strongly advection-dominated problems are better handled with SUPG or Galerkin/least-squares.