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A posteriori error estimates for finite element exterior calculus: the de Rham complex. (English) Zbl 1308.65187
In a fairly sophisticated framework, i.e., the Hilbert complex structure for finite element exterior calculus, the authors rigorously establish a posteriori upper bounds for errors in approximation to the Hodge-de Rham-Laplace problems. Some elementwise efficiency results are also carried out. Eventually, the authors show how their results apply to several specific examples from the three-dimensional de Rham complex.

65N15 Error bounds for boundary value problems involving PDEs
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
58A12 de Rham theory in global analysis
58A14 Hodge theory in global analysis
58A15 Exterior differential systems (Cartan theory)
58J05 Elliptic equations on manifolds, general theory
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