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Journal Articles Mathematical Methods in the Applied Sciences Year : 2016

The Laplace equation in 3-D domains with cracks: Dual shadows with log terms and extraction of corresponding edge flux intensity functions

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Abstract

The singular solution of the Laplace equation with a straight-crack is represented by a series of eigenpairs, shadows and their associated edge flux intensity functions (EFIFs). We address the computation of the EFIFs associated with the integer eigenvalues by the quasi dual function method (QDFM).The QDFM is based on the dual eigenpairs and shadows, and we show that the dual shadows associated with the integer eigenvalues contain logarithmic terms. These are then used with the QDFM to extract EFIFs from p-version finite element solutions. Numerical examples are provided. Dedicated to the 65th birthday of prof. Martin Costabel.
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Dates and versions

hal-01111593 , version 1 (06-07-2015)

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Samuel Shannon, Victor Péron, Zohar Yosibash. The Laplace equation in 3-D domains with cracks: Dual shadows with log terms and extraction of corresponding edge flux intensity functions. Mathematical Methods in the Applied Sciences, 2016, ⟨10.1002/mma.3562⟩. ⟨hal-01111593⟩
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