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.
Original language | English (US) |
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Pages (from-to) | 1777-1800 |
Number of pages | 24 |
Journal | Journal of Scientific Computing |
Volume | 79 |
Issue number | 3 |
DOIs | |
State | Published - Jun 15 2019 |
Bibliographical note
Publisher Copyright:© 2019, Springer Science+Business Media, LLC, part of Springer Nature.
Keywords
- Hybridizable discontinuous Galerkin method
- Interpolatory method
- Newton iteration