A Superconvergent Local Discontinuous Galerkin Method for Nonlinear Fourth-Order Boundary-Value Problems.
In: International Journal of Computational Methods, Jg. 17 (2020-09-01), Heft 7, S. N.PAG- (31S.)
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Zugriff:
In this paper, we present a superconvergent local discontinuous Galerkin (LDG) method for nonlinear fourth-order boundary-value problems (BVPs) of the form u (4) + f (x , u) = 0. We prove optimal L 2 error estimates for the solution and for the three auxiliary variables that approximate the first, second, and third-order derivatives. The order of convergence is proved to be p + 1 , when piecewise polynomials of degree at most p are used. Our numerical experiments demonstrate optimal rates of convergence. We further prove that the derivatives of the LDG solutions are superconvergent with order p + 1 toward the derivatives of Gauss–Radau projections of the exact solutions. Finally, we prove that the LDG solutions are superconvergent with order p + 3 / 2 toward Gauss–Radau projections of the exact solutions. Our numerical results indicate that the numerical order of superconvergence rate is p + 2. Our proofs are valid for arbitrary regular meshes using piecewise polynomials of degree p ≥ 1 and for the classical sets of boundary conditions. Several computational examples are provided to validate the theoretical results. [ABSTRACT FROM AUTHOR]
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Titel: |
A Superconvergent Local Discontinuous Galerkin Method for Nonlinear Fourth-Order Boundary-Value Problems.
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Autor/in / Beteiligte Person: | Baccouch, Mahboub |
Zeitschrift: | International Journal of Computational Methods, Jg. 17 (2020-09-01), Heft 7, S. N.PAG- (31S.) |
Veröffentlichung: | 2020 |
Medientyp: | academicJournal |
ISSN: | 0219-8762 (print) |
DOI: | 10.1142/S021987621950035X |
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