A posteriori error estimates for finite element exterior calculus: the de Rham complex (Q486694)

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.