Analysis of one-dimensional Helmholtz equation with PML boundary

Authors:
Taeyoung Ha;Imbunm Kim
Affiliations:
Department of Mathematical Sciences, Seoul National University, San 56-1, Shinrim-dong, Kwanakgu, Seoul 151-747, Republic of Korea;Department of Mathematical Sciences, Seoul National University, San 56-1, Shinrim-dong, Kwanakgu, Seoul 151-747, Republic of Korea
Venue:
Journal of Computational and Applied Mathematics
Year:
2007

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Abstract

In this paper, the linear conforming finite element method for the one-dimensional Berenger's PML boundary is investigated and well-posedness of the given equation is discussed. Furthermore, optimal error estimates and stability in the L^2 or H^1-norm are derived under the assumption that h, h^2@w^2 and h^2@w^3 are sufficiently small, where h is the mesh size and @w denotes a fixed frequency. Numerical examples are presented to validate the theoretical error bounds.