Benchmark results for testing adaptive finite element eigenvalue procedures

Authors:
Stefano Giani;Luka Grubišić;Jeffrey S. Ovall
Affiliations:
School of Mathematical Sciences University of Nottingham, University Park, Nottingham, NG7 2RD, United Kingdom;University of Zagreb, Department of Mathematics, Bijenička 30, 10000 Zagreb, Croatia;University of Kentucky, Department of Mathematics, Patterson Office Tower 761, Lexington, KY 40506-0027, USA
Venue:
Applied Numerical Mathematics
Year:
2012

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Abstract

A discontinuous Galerkin method, with hp-adaptivity based on the approximate solution of appropriate dual problems, is employed for highly-accurate eigenvalue computations on a collection of benchmark examples. After demonstrating the effectivity of our computed error estimates on a few well-studied examples, we present results for several examples in which the coefficients of the partial-differential operators are discontinuous. The problems considered here are put forward as benchmarks upon which other adaptive methods for computing eigenvalues may be tested, with results compared to our own.