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- W2795290622 abstract "The Nitsche method is a method of weak imposition of the inhomogeneous Dirichlet boundary conditions for partial differential equations. This paper explains stability and convergence study of the Nitsche method applied to evolutionary diffusion-advection-reaction equations. We mainly discuss a general space semidiscrete scheme including not only the standard finite element method but also Isogeometric Analysis. Our method of analysis is a variational one that is a popular method for studying elliptic problems. The variational method enables us to obtain the best approximation property directly. Actually, results show that the scheme satisfies the inf-sup condition and Galerkin orthogonality. Consequently, the optimal order error estimates in some appropriate norms are proven under some regularity assumptions on the exact solution. We also consider a fully discretized scheme using the backward Euler method. Numerical example demonstrate the validity of those theoretical results." @default.
- W2795290622 created "2018-04-06" @default.
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- W2795290622 date "2018-12-01" @default.
- W2795290622 modified "2023-10-17" @default.
- W2795290622 title "The inf-sup condition and error estimates of the Nitsche method for evolutionary diffusion–advection-reaction equations" @default.
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- W2795290622 doi "https://doi.org/10.1007/s13160-018-0338-4" @default.
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