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Resolving phase transitions with discontinuous Galerkin methods
SciPost Physics Core, 2023 We demonstrate the applicability and advantages of Discontinuous Galerkin (DG) schemes in the context of the Functional Renormalization Group (fRG). We investigate the $O(N)$-model in the large $N$ limit.
Eduardo Grossi, Nicolas Wink
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Journal of Harbin University of Science and Technology, 2022 The equivalence between direct flux reconstruction method and discontinuous Galerkin method for solving parabolic equation and convection-diffusion equation is studied.
BI Hui, LIU Lei
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Non-Hydrostatic Discontinuous/Continuous Galerkin Model for Wave Propagation, Breaking and Runup
Computation, 2021 This paper presents a new depth-integrated non-hydrostatic finite element model for simulating wave propagation, breaking and runup using a combination of discontinuous and continuous Galerkin methods.
Lucas Calvo +3 more
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Comparison of implicit time-discretization schemes for hybridized discontinuous Galerkin methods
Applied and Computational Mechanics, 2022 The present study is focused on the application of two families of implicit time-integration schemes for general time-dependent balance laws of convection-diffusion-reaction type discretized by a hybridized discontinuous Galerkin method in space, namely ...
Levý T., May G.
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Numerical approximation of time-fractional Burgers-type equation
Advances in Difference Equations, 2020 In this work, we analyze and test a local discontinuous Galerkin method for solving the Burgers-type equation. The proposed numerical method, which is high-order accurate, is based on a finite difference scheme in time and local discontinuous Galerkin ...
Miaomiao Yang
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Convergence Analysis of the Lowest Order Weakly Penalized Adaptive Discontinuous Galerkin Methods [PDF]
, 2012 In this article, we prove convergence of the weakly penalized adaptive discontinuous Galerkin methods. Unlike other works, we derive the contraction property for various discontinuous Galerkin methods only assuming the stabilizing parameters are large ...
Gudi, Thirupathi, Guzmán, Johnny
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Well-Balanced High-Order Discontinuous Galerkin Methods for Systems of Balance Laws
Mathematics, 2021 This work introduces a general strategy to develop well-balanced high-order Discontinuous Galerkin (DG) numerical schemes for systems of balance laws.
Ernesto Guerrero Fernández +2 more
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Advanced Modeling and Simulation in Engineering Sciences, 2019 This research work presents some comparisons and analyses of the time discontinuous space–time Galerkin method and the space discontinuous Galerkin method applied to elastic wave propagation in anisotropic and heterogeneous media.
Bing Tie
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Steady-State Simulation of Semiconductor Devices Using Discontinuous Galerkin Methods
IEEE Access, 2020 Design of modern nanostructured semiconductor devices often calls for simulation tools capable of modeling arbitrarily-shaped multiscale geometries. In this work, to this end, a discontinuous Galerkin (DG) method-based framework is developed to simulate ...
Liang Chen, Hakan Bagci
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Quail: A lightweight open-source discontinuous Galerkin code in Python for teaching and prototyping
SoftwareX, 2022 In this paper, we present Quail, a lightweight discontinuous Galerkin solver written in Python. The aim of this code is to serve not only as a teaching tool for newcomers to the rapidly growing field, but also as a prototyping platform for testing ...
Eric J. Ching +3 more
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