Maximum-norm stability of the finite element Ritz projection under mixed boundary conditions
نویسندگان
چکیده
As a model of the second order elliptic equation with non-trivial boundary conditions, we consider the Laplace equation with mixed Dirichlet and Neumann boundary conditions on convex polygonal domains. Our goal is to establish that finite element discrete harmonic functions with mixed Dirichlet and Neumann boundary conditions satisfy a weak (Agmon-Miranda) discrete maximum principle, and then prove the stability of the Ritz projection with mixed boundary conditions in L∞ norm. Such results have a number of applications, but are not available in the literature. Our proof of the maximum-norm stability of the Ritz projection is based on converting the mixed boundary value problem to a pure Neumann problem, which is of independent interest.
منابع مشابه
Maximum-norm stability of the finite element Ritz projection with mixed boundary conditions
In this paper we prove that finite element discrete harmonic functions with mixed Dirichlet and Neumann boundary conditions satisfy a weak (Agmon-Miranda) maximum principle on convex polygonal domains. Using this result, we establish the stability of the Ritz projection with mixed boundary conditions in L∞ norm up to a logarithmic term.
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