Memorandum 1810
Adaptive finite element techniques for the Maxwell equations using implicit a posteriori error estimates
D. Harutyunyan, F. Izsák, J.J.W. van der Vegt & M.A. Botchev
Abstract:
For the adaptive solution of the Maxwell equations
on three-dimensional domains with Nédélec edge finite element methods,
we consider an implicit a posteriori error estimation technique.
On each element of the tessellation
an equation
for the error is formulated and solved with a properly
chosen local finite element basis. We show that the discrete
bilinear form of the local problems
satisfies an inf-sup condition ensuring the well posedness
of the error equations.
An adaptive algorithm is developed based on the estimated error.
We show that the
method accurately predicts the regions in the domain with a
larger error. The performance of the method is tested on various problems
on non-convex domains with non-smooth boundaries. The numerical results show
an accurate approximation of the true error.
On the meshes generated adaptively with the help of
the implicit a posteriori error estimation technique an
error is obtained which is smaller than on globally
refined meshes.
Moreover, the convergence of the error on the locally adapted meshes
is faster than that on the globally refined mesh.
Keywords:
Maxwell equations, h-adaptive methods, implicit error estimates, Nédélec edge tetrahedral elements
Mathematics Subject Classification: 35Q60, 65N30, 35B99
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