@article{17960,
  author = {Jana Brun{\'a}tov{\'a} and J{\o}rgen Dokken and Kristian Valen-Sendstad and Jaroslav Hron},
  title = {On the numerical evaluation of wall shear stress using the finite element method},
  abstract = {Wall shear stress (WSS) is a crucial hemodynamic quantity extensively studied in cardiovascular research,yet its numerical computation is not straightforward. This work aims to compare WSS results obtained fromtwo different finite element discretizations, quantify the differences between continuous and discontinuousstresses, and introduce a novel method for WSS evaluation through the formulation of a boundary-fluxproblem.Two benchmark problems are considered {\textendash} a 2D Stokes flow on a unit square and a 3D Poiseuille flowthrough a cylindrical pipe. These are followed by investigations of steady-state Navier{\textendash}Stokes flow in twopatient-specific aneurysms. The study focuses on P1/P1 stabilized and Taylor{\textendash}Hood P2/P1 mixed finiteelements for velocity and pressure. WSS is computed using either the proposed boundary-flux method or asa projection of tangential traction onto First order Lagrange (P1), Discontinuous Galerkin first order (DG-1),or Discontinuous Galerkin zero order (DG-0) space.For the P1/P1 stabilized element, the boundary-flux and P1 projection methods yielded equivalent results.With the P2/P1 element, the boundary-flux evaluation demonstrated faster convergence in the Poiseuilleflow example but showed increased sensitivity to pressure field inaccuracies in patient-specific geometriescompared to the projection method. In patient-specific cases, the P2/P1 element exhibited superior robustnessto mesh size when evaluating average WSS and low shear area (LSA), outperforming the P1/P1 stabilizedelement.Projecting discontinuous finite element results into continuous spaces can introduce artifacts, such as theGibbs phenomenon. Consequently, it becomes crucial to carefully select the finite element space for boundarystress calculations {\textendash} not only in applications involving WSS computations for aneurysms.},
  year = {2024},
  journal = {Preprint},
  publisher = {Arxiv},
  doi = {10.48550/arXiv.2501.02987},
}