# Adaptive Hybridizable Discontinuous Galerkin discretization of the Grad-Shafranov equation by extension from polygonal subdomains

@article{SanchezVizuet2019AdaptiveHD, title={Adaptive Hybridizable Discontinuous Galerkin discretization of the Grad-Shafranov equation by extension from polygonal subdomains}, author={Tonatiuh S'anchez-Vizuet and Manuel E. Solano and Antoine J. Cerfon}, journal={Comput. Phys. Commun.}, year={2019}, volume={255}, pages={107239} }

## 9 Citations

### Error Analysis of an Unfitted HDG Method for a Class of Non-linear Elliptic Problems

- Computer Science, MathematicsJournal of Scientific Computing
- 2022

A priori error estimates are provided showing that the discrete solution will have optimal order of convergence as long as the distance between the curved boundary and the computational boundary remains of the same order of magnitude as the mesh parameter.

### Error Analysis of an Unfitted HDG Method for a Class of Non-linear Elliptic Problems

- Computer Science, MathematicsJ. Sci. Comput.
- 2022

A priori error estimates are provided showing that the discrete solution will have optimal order of convergence as long as the distance between the curved boundary and the computational boundary remains of the same order of magnitude as the mesh parameter.

### An adaptive discontinuous Petrov-Galerkin method for the Grad-Shafranov equation

- Computer ScienceSIAM J. Sci. Comput.
- 2020

In this work, we propose and develop an arbitrary-order adaptive discontinuous Petrov-Galerkin (DPG) method for the nonlinear Grad-Shafranov equation. An ultraweak formulation of the DPG scheme for…

### Adaptive DPG for Grad-Shafranov

- Computer Science
- 2020

In this work, we propose and develop an arbitrary-order adaptive discontinuous Petrov-Galerkin (DPG) method for the nonlinear Grad-Shafranov equation. An ultraweak formulation of the DPG scheme for…

### A parallel cut-cell algorithm for the free-boundary Grad-Shafranov problem

- Computer ScienceSIAM Journal on Scientific Computing
- 2021

A parallel cut-cell algorithm to solve the free boundary problem of the Grad-Shafranov equation in an irregular bounded domain and its important aspects include a searching algorithm for the magnetic axis and separatrix, a surface integral along the irregular boundary to determine the boundary values.

### HDGlab: An Open-Source Implementation of the Hybridisable Discontinuous Galerkin Method in MATLAB

- Computer ScienceArchives of Computational Methods in Engineering
- 2020

The main goal is to provide a detailed description of both the HDG method for elliptic problems and its implementation available in HDGlab, an open source MATLAB implementation of the hybridisable discontinuous Galerkin (HDG) method to make this relatively new advanced discretisation method more accessible to the computational engineering community.

### HDGlab: An Open-Source Implementation of the Hybridisable Discontinuous Galerkin Method in MATLAB

- Computer ScienceArXiv
- 2020

This paper presents HDGlab, an open source MATLAB implementation of the hybridisable discontinuous Galerkin (HDG) method, which implements high-order polynomial shape functions up to degree nine, with both equally-spaced and Fekete nodal distributions.

### Afternote to “Coupling at a Distance”: Convergence Analysis and A Priori Error Estimates

- MathematicsComput. Methods Appl. Math.
- 2022

This article proves the convergence of a relaxation of the algorithm and providing a priori error estimates for the numerical solution to solve an exterior Dirichlet problem.

### A priori and a posteriori error analysis of an unfitted HDG method for semi-linear elliptic problems

- Computer Science, MathematicsNumerische Mathematik
- 2021

An HDG discretization is shown to be optimal under mild assumptions related to the non-linear source term and the distance between the boundaries of the polygonal subdomain.

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