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Prof.dr.ir. Jaap J.W. van der Vegt (University of Twente)
| Speaker: |
Prof.dr.ir. Jaap J.W. van
der Vegt (University of Twente)
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| Date: |
Wednesday March 28, 2007 |
| Title: |
Solution
Adaptive Finite Element Discretizations for the Maxwell Equations
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Abstract
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The accuracy and efficiency of numerical
algorithms for the solution of the Maxwell equations can be
significantly improved using adaptive finite element methods. In
particular, near sharp corners and on non-convex domains the solution
has singularities which can be captured more efficiently with a
solution adaptive mesh. A key element in any adaptive scheme is the
control of the adaptation process. In this presentation we will discuss
an implicit a posteriori error estimation technique for the adaptive
solution of the
Maxwell equations on three-dimensional domains using
Nédélec edge finite elements. On each element of the
tessellation an equation for the error is formulated and solved with a
properly chosen local finite element basis. The local error
distribution is then used to generate a new mesh to obtain a more
accurate numerical solution. A nice feature of the implicit a
posteriori error estimates is that they do not contain unknown
coefficients, as frequently occurs with residual based error estimators
and improves the reliability of the adaptive algorithm. After the
definition of the main algorithm we will first discuss some of its
theoretical properties. In particular, we will show that the discrete
bilinear form of the local problems satisfies an inf-sup condition
which ensures the well posedness of the error equations. Also, the
relation of the estimated error to the true error will be discussed. In
the second part of this presentation the performance of the method is
demonstrated on various problems, including non-convex domains with
non-smooth boundaries. The numerical results show that the estimated
error, computed by the implicit a posteriori error estimation
technique, correlates well with the actual error.
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