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Journal of Scientific Computing

Erschienen in:

22.01.2019

Interpolatory HDG Method for Parabolic Semilinear PDEs

verfasst von: Bernardo Cockburn, John R. Singler, Yangwen Zhang

Erschienen in: Journal of Scientific Computing | Ausgabe 3/2019

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Abstract

We propose the interpolatory hybridizable discontinuous Galerkin (Interpolatory HDG) method for a class of scalar parabolic semilinear PDEs. The Interpolatory HDG method uses an interpolation procedure to efficiently and accurately approximate the nonlinear term. This procedure avoids the numerical quadrature typically required for the assembly of the global matrix at each iteration in each time step, which is a computationally costly component of the standard HDG method for nonlinear PDEs. Furthermore, the Interpolatory HDG interpolation procedure yields simple explicit expressions for the nonlinear term and Jacobian matrix, which leads to a simple unified implementation for a variety of nonlinear PDEs. For a globally-Lipschitz nonlinearity, we prove that the Interpolatory HDG method does not result in a reduction of the order of convergence. We display 2D and 3D numerical experiments to demonstrate the performance of the method.

Vorheriger Artikel An Effective Dissipation-Preserving Fourth-Order Difference Solver for Fractional-in-Space Nonlinear Wave Equations

Nächster Artikel A Jacobi Spectral Method for Solving Multidimensional Linear Volterra Integral Equation of the Second Kind

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Titel: Interpolatory HDG Method for Parabolic Semilinear PDEs
verfasst von: Bernardo Cockburn
John R. Singler
Yangwen Zhang
Publikationsdatum: 22.01.2019
Verlag: Springer US
Erschienen in: Journal of Scientific Computing / Ausgabe 3/2019
Print ISSN: 0885-7474
Elektronische ISSN: 1573-7691
DOI: https://doi.org/10.1007/s10915-019-00911-8

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