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A note on the design of \(hp\)-adaptive finite element methods for elliptic partial differential equations. (English) Zbl 1074.65131
The design of an automatic mesh modification strategy that is capable of exploiting both local \(h\)- and \(p\)-refinement is studied. The main focus of the paper is to provide a complete account of the design of a fully automatic \(hp\)-adaptive algorithm for the finite element approximation to a one-dimensional reaction-diffusion equation [cf. P. K. Moore, Numer. Math. 94, 367–401 (2003; Zbl 1033.65067)]. Some numerical experiments to highlight the practical performance of the proposed \(hp\)-adaptive finite element algorithm are also given.

MSC:
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N15 Error bounds for boundary value problems involving PDEs
35J25 Boundary value problems for second-order elliptic equations
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