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}
}
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9 Citations
Highly Influential Citations
2
Background Citations
6
Methods Citations
7
Results Citations
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9 Citations

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

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

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.

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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

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

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

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

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

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

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.

References

SHOWING 1-10 OF 57 REFERENCES

A Hybridizable Discontinuous Galerkin solver for the Grad-Shafranov equation

A mimetic spectral element solver for the Grad-Shafranov equation

Solving Dirichlet Boundary-value Problems on Curved Domains by Extensions from Subdomains

A technique for numerically solving Dirichlet boundary-value problems for second-order elliptic equations on domains $\Omega$ with curved boundaries is presented and it is found that when using polynomial approximations of degree $k$ on the polyhedral subdomains, both the scalar and vector unknowns converge with the optimal order.

Contraction property of adaptive hybridizable discontinuous Galerkin methods

The contraction property between consecutive loops of adaptive hybridizable discontinuous Galerkin methods for the Poisson problem with homogeneous Dirichlet condition is established and the lifting of trace residuals from inter-element boundaries to element interiors is lifted.

Solving the Grad-Shafranov equation with spectral elements

Quasi-static free-boundary equilibrium of toroidal plasma with CEDRES++: Computational methods and applications

We present a comprehensive survey of the various computational methods in CEDRES++ for finding equilibria of toroidal plasma. Our focus is on free-boundary plasma equilib-ria, where either poloidal…

Unified Hybridization of Discontinuous Galerkin, Mixed, and Continuous Galerkin Methods for Second Order Elliptic Problems

A unifying framework for hybridization of finite element methods for second order elliptic problems is introduced, thanks to which it is possible to see how to devise novel methods displaying very localized and simple mortaring techniques, as well as methods permitting an even further reduction of the number of globally coupled degrees of freedom.

Quasi-static Free-Boundary Equilibrium of Toroidal Plasma with CEDRES + + : Computational Methods and Applications

We present a comprehensive survey of the various computational methods in CEDRES++ for finding equilibria of toroidal plasma. Our focus is on free-boundary plasma equilibria, where either poloidal…

A BASIC CONVERGENCE RESULT FOR CONFORMING ADAPTIVE FINITE ELEMENTS

We consider the approximate solution with adaptive finite elements of a class of linear boundary value problems, which includes problems of "saddle point" type. For the adaptive algorithm we assume…

A fast, high-order solver for the Grad-Shafranov equation

...