Journal
JOURNAL OF SCIENTIFIC COMPUTING
Volume 79, Issue 3, Pages 1777-1800Publisher
SPRINGER/PLENUM PUBLISHERS
DOI: 10.1007/s10915-019-00911-8
Keywords
Hybridizable discontinuous Galerkin method; Interpolatory method; Newton iteration
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Funding
- National Science Foundation [DMS-1217122]
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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.
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