Multidomain Legendre-Galerkin Chebyshev collocation least squares method for one-dimensional problems with two nonhomogeneous jump conditions

ABSTRACT

The multidomain Legendre-Galerkin Chebyshev collocation least squares method is developed for one-dimensional problems with two nonhomogeneous jump conditions. The original problem is rewritten as an equivalent first-order system by introducing a flux variable. The scheme is based on the Legendre Galerkin method, but Chebyshev-Gauss-Lobatto points interpolation are applied in computation of the piecewise smooth variable coefficient and the right hand side terms. By choosing appropriate base functions to deal with interfaces, the proposed method can be implemented in parallel. The coercivity and continuity of the method are proved and an error estimate in a block ${\tilde{H}}^1$-norm is derived. Numerical examples are given to validate the efficiency and accuracy.

KEYWORDS:

• Nonhomogeneous jump conditions
• Legendre Galerkin
• Chebyshev collocation
• least squares

AMS SUBJECT CLASSIFICATIONS:

• 35F25
• 65M70
• 65L06

Acknowledgments

We would like to thank the anonymous referees for their valuable comments and suggestions which improve the manuscript.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work is supported by the National Natural Science Foundation of China (No. 11701119, 11601331), the Natural Science Foundation of Guangxi (No. 2017GXNSFBA198053), and the open fund of Guangxi Key laboratory of hybrid computation and IC design analysis (No. HCIC201607).