Nitsche
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Related Articles from SNS
A Nitsche method for incompressible fluids with general dynamic boundary conditions
arXiv:2502.09550v2 Announce Type: replace Abstract: Both Newtonian and non-Newtonian fluids may exhibit complex slip behaviour at the boundary. We examine a broad class of slip boundary conditions that generalises the commonly used Navier slip, perfect slip, stick-slip and Tresca friction boundary conditions. In particular, set-valued, nonmonotone, noncoercive and dynamic relations may occur.
Kernel Methods in the Deep Ritz framework: Theory and practice
Announce Type: replace Abstract: In this contribution, kernel approximations are applied as ansatz functions within the Deep Ritz method. This allows to approximate weak solutions of elliptic partial differential equations with weak enforcement of boundary conditions using Nitsche's method. A priori error estimates are proven in different norms leveraging both standard results for weak solutions of elliptic equations and well-established convergence results for kernel methods.
Uniform Schwarz Preconditioners for Variable-Degree $hp$ Finite Element Interface Problems
arXiv:2606.03141v1 Announce Type: new Abstract: We construct $h$- and $p$-robust, degree-preserving space decompositions and additive Schwarz preconditioners for variable-degree $hp$ finite element discretizations of reaction-diffusion and fitted-interface problems. On conforming simplicial meshes in arbitrary dimension, the single-domain result allows an arbitrary elementwise degree distribution subject only to $p_K\ge1$. A minimal-average Falk--Winther bubble transform is introduced by...