p-adaptive discontinuous Galerkin method for the shallow water equations with a parameter-free error indicator

Faghih-Naini, Sara; Aizinger, Vadym

doi:10.1007/s13137-022-00208-3

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2023

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Cited by 3 publications

References 37 publications

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Shallow Water DG Simulations on FPGAs: Design and Comparison of a Novel Code Generation Pipeline

Alt,

Kenter,

Faghih-Naini

et al. 2023

Lecture Notes in Computer Science

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Shallow Water DG Simulations on FPGAs: Design and Comparison of a Novel Code Generation Pipeline

Alt,

Kenter,

Faghih-Naini

et al. 2023

Lecture Notes in Computer Science

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p-adaptive discontinuous Galerkin method for the shallow water equations with a parameter-free error indicator

Faghih-Naini

Aizinger

2022

Int J Geomath

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We propose a p-adaptive quadrature-free discontinuous Galerkin method for the shallow water equations based on a computationally efficient adaptivity indicator which works without any problem-dependent parameters. The error and smoothness of the solution are detected using the information collected for slope limiting and, for piecewise constant discretizations, by carrying out a reconstruction procedure. The accuracy and robustness of the new scheme are evaluated using several benchmarks and compared to other adaptivity indicators. Our results indicate that the proposed indicator finds a good balance between solution quality and computational overhead.

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An h-Adaptive Poly-Sinc-Based Local Discontinuous Galerkin Method for Elliptic Partial Differential Equations

Khalil

Baumann

2023

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For the purpose of solving elliptic partial differential equations, we suggest a new approach using an h-adaptive local discontinuous Galerkin approximation based on Sinc points. The adaptive approach, which uses Poly-Sinc interpolation to achieve a predetermined level of approximation accuracy, is a local discontinuous Galerkin method. We developed an a priori error estimate and demonstrated the exponential convergence of the Poly-Sinc-based discontinuous Galerkin technique, as well as the adaptive piecewise Poly-Sinc method, for function approximation and ordinary differential equations. In this paper, we demonstrate the exponential convergence in the number of iterations of the a priori error estimate derived for the local discontinuous Galerkin technique under the condition that a reliable estimate of the precise solution of the partial differential equation at the Sinc points exists. For the purpose of refining the computational domain, we employ a statistical strategy. The numerical results for elliptic PDEs with Dirichlet and mixed Neumann-Dirichlet boundary conditions are demonstrated to validate the adaptive greedy Poly-Sinc approach

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p-adaptive discontinuous Galerkin method for the shallow water equations with a parameter-free error indicator

Cited by 3 publications

References 37 publications

Shallow Water DG Simulations on FPGAs: Design and Comparison of a Novel Code Generation Pipeline

Shallow Water DG Simulations on FPGAs: Design and Comparison of a Novel Code Generation Pipeline

p-adaptive discontinuous Galerkin method for the shallow water equations with a parameter-free error indicator

An h-Adaptive Poly-Sinc-Based Local Discontinuous Galerkin Method for Elliptic Partial Differential Equations

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