18,713 research outputs found
A Duality Approach to Error Estimation for Variational Inequalities
Motivated by problems in contact mechanics, we propose a duality approach for
computing approximations and associated a posteriori error bounds to solutions
of variational inequalities of the first kind. The proposed approach improves
upon existing methods introduced in the context of the reduced basis method in
two ways. First, it provides sharp a posteriori error bounds which mimic the
rate of convergence of the RB approximation. Second, it enables a full
offline-online computational decomposition in which the online cost is
completely independent of the dimension of the original (high-dimensional)
problem. Numerical results comparing the performance of the proposed and
existing approaches illustrate the superiority of the duality approach in cases
where the dimension of the full problem is high.Comment: 21 pages, 8 figure
Simultaneous Reduced Basis Approximation of Parameterized Elliptic Eigenvalue Problems
The focus is on a model reduction framework for parameterized elliptic
eigenvalue problems by a reduced basis method. In contrast to the standard
single output case, one is interested in approximating several outputs
simultaneously, namely a certain number of the smallest eigenvalues. For a fast
and reliable evaluation of these input-output relations, we analyze a
posteriori error estimators for eigenvalues. Moreover, we present different
greedy strategies and study systematically their performance. Special attention
needs to be paid to multiple eigenvalues whose appearance is
parameter-dependent. Our methods are of particular interest for applications in
vibro-acoustics
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