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research-article

A meshless superconvergent stabilized collocation method for linear and nonlinear elliptic problems with accuracy analysis

Published: 15 September 2024 Publication History

Abstract

The stabilized collocation method (SCM) is a promising meshless collocation method that can overcome the instability defects in the classical direct collocation method. To improve the performance of the SCM, a superconvergent stabilized collocation method (SSCM) is developed in this paper for linear and nonlinear elliptic problems through the use of the moving least squares (MLS) approximation and its smoothed derivatives. Accuracy of the SSCM and the SCM is analyzed with an emphasis on the influence of boundary conditions, and precise error measures are presented for different types of boundary conditions. Numerical results validate the superconvergence of the SSCM and confirm the theoretical analysis.

Highlights

A superconvergent stabilized collocation method is developed for linear and nonlinear elliptic problems.
Theoretical accuracy of the method is analyzed detailedly.
Theoretical and numerical results reveal that the method possesses superconvergence property.

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Information

Published In

cover image Applied Mathematics and Computation
Applied Mathematics and Computation  Volume 477, Issue C
Sep 2024
370 pages

Publisher

Elsevier Science Inc.

United States

Publication History

Published: 15 September 2024

Author Tags

  1. Meshless methods
  2. Stabilized collocation method
  3. Nonlinear elliptic problem
  4. Error analysis
  5. Boundary effect
  6. Superconvergence

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