A penalty free Nitsche type method for the weak imposition of boundary conditions in compressible and incompressible elasticity

2014/07/08 by Thomas Boiveau, Boiveau, Thomas, Erik Burman +1 · 2 citations
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #Differential Equations and Numerical Methods #FOS: Mathematics #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.1407.2229

openalex publication_date 2014/07/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we study the stability of the nonsymmetric version of Nitsche's method without penalty for compressible and incompressible elasticity. For the compressible case we prove the convergence of the error in the H¹- and L²-norms. In the incompressible case we use a Galerkin least squares pressure stabilization and we prove the convergence in the H¹-norm for the velocity and convergence of the pressure in the L²-norm.

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• Gap-SBM: A New Conceptualization of the Shifted Boundary Method with Optimal Convergence for the Neumann and Dirichlet Problems
• Fitted and unfitted domain decomposition using penalty free Nitsche method for the Poisson problem with discontinuous material parameters

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