TY - JOUR
T1 - Efficient and Accurate Legendre Spectral Element Methods for One-Dimensional Higher Order Problems
AU - Zhang , Yang
AU - Yu , Xuhong
AU - Wang , Zhongqing
JO - Numerical Mathematics: Theory, Methods and Applications
VL - 2
SP - 461
EP - 487
PY - 2021
DA - 2021/01
SN - 14
DO - http://doi.org/10.4208/nmtma.OA-2020-0082
UR - https://global-sci.org/intro/article_detail/nmtma/18607.html
KW - Legendre spectral element methods, higher order differential equations, Sobolev
orthogonal/biorthogonal basis functions, high oscillatory or steep gradient solutions.
AB - <p style="text-align: justify;">Efficient and accurate Legendre spectral element methods for solving one-dimensional higher order differential equations with high oscillatory or steep gradient solutions are proposed. Some Sobolev orthogonal/biorthogonal basis functions
corresponding to each subinterval are constructed, which reduce the non-zero entries of linear systems and computational cost. Numerical experiments exhibit the
effectiveness and accuracy of the suggested approaches.&nbsp;</p>