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Journal of Scientific Computing

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30-10-2018

Enriched Spectral Methods and Applications to Problems with Weakly Singular Solutions

Authors: Sheng Chen, Jie Shen

Published in: Journal of Scientific Computing | Issue 3/2018

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Abstract

Usual spectral methods are very effective for problems with smooth solutions, but their accuracy will be severely limited if solution of the underlying problems exhibits singular behavior. We develop in this paper enriched spectral-Galerkin methods (ESG) to deal with a class of problems for which the form of leading singular solutions can be determined. Several strategies are developed to overcome the ill conditioning due to the addition of singular functions as basis functions, and to efficiently solve the approximate solution in the enriched space. We validate ESG by solving a variety of elliptic problems with weakly singular solutions.

previous article On the Conservation of Fractional Nonlinear Schrödinger Equation’s Invariants by the Local Discontinuous Galerkin Method

next article An Adaptive Staggered Discontinuous Galerkin Method for the Steady State Convection–Diffusion Equation

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Title: Enriched Spectral Methods and Applications to Problems with Weakly Singular Solutions
Authors: Sheng Chen
Jie Shen
Publication date: 30-10-2018
Publisher: Springer US
Published in: Journal of Scientific Computing / Issue 3/2018
Print ISSN: 0885-7474
Electronic ISSN: 1573-7691
DOI: https://doi.org/10.1007/s10915-018-0862-z

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