This paper presents the analysis and computation of an adaptive Dirichlet-to-Neumann (DtN) finite element method for solving the two-dimensional thermoelastic wave scattering problem. Using the Helmholtz decomposition, the vectorial coupled governing equations of thermoelastic waves are transformed into three Helmholtz equations for scalar potentials with distinct wavenumbers. The DtN map and the corresponding transparent boundary condition are derived through Fourier series expansions of the potentials. Well-posedness results are established for both the variational problem and its truncated formulation, which accounts for the truncation of the DtN map. Both a priori and a posteriori error estimates are established, accounting for the truncation of the DtN operator and the finite element discretization. Numerical experiments are conducted to validate the theoretical findings.

Publication:

Journal of Computational Physics 534 (2025) 114016

http://dx.doi.org/10.1016/j.jcp.2025.114016

Author:

Yu Wang

School of Mathematical Sciences, University of Electronic Science and Technology of China, Sichuan, 611731, China

wy22@std.uestc.edu.cn

Peijun Li

SKLMS, ICMSEC, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China

lipeijun@lsec.cc.ac.cn

Liwei Xu

School of Mathematical Sciences, University of Electronic Science and Technology of China, Sichuan, 611731, China

xul@uestc.edu.cn

Tao Yin

SKLMS, Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China

Corresponding author

yintao@lsec.cc.ac.cn