Balanced norm estimates for rp-Finite Element Methods applied to singularly perturbed fourth order boundary value problems
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We establish robust exponential convergence for rp-Finite Element Methods (FEMs) applied to fourth order singularly perturbed boundary value problems, in a balanced norm which is stronger than the usual energy norm associated with the problem. As a corollary, we get robust exponential convergence in the maximum norm. r p FEMs are simply p FEMs with possible repositioning of the (fixed number of) nodes. This is done for a C^1 Galerkin FEM in 1-D, and a C^0 mixed FEM in 2-D over domains with smooth boundary. In both cases we utilize the Spectral Boundary Layer mesh.
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