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Adaptive discontinuous Galerkin methods on surfaces [article]

Andreas Dedner, Pravin Madhavan
2014 arXiv   pre-print
We also present a novel "geometric" driven refinement strategy for PDEs on surfaces which considerably improves the performance of the method on complex surfaces.  ...  We present a dual weighted residual-based a posteriori error estimate for a discontinuous Galerkin (DG) approximation of a linear second-order elliptic problem on compact smooth connected and oriented  ...  Larsson & Larson (2013) have considered a continuous/discontinuous Galerkin method for a fourth order elliptic PDE on surfaces.  ... 
arXiv:1402.2117v1 fatcat:ql7esi6vz5by7esmhn7ktgsb74

Page 1262 of Mathematical Reviews Vol. , Issue 2002B [page]

2002 Mathematical Reviews  
Hu, Some remarks on the accuracy of a discontinuous Galerkin method (407-412).  ...  Teresco, Software for the parallel adaptive solution of conservation laws by discontinuous Galerkin methods (113-123); Pierre A. Gremaud and John V.  ... 

Research on the Discontinuous Galerkin Method for Water Flow of Aeration Zone

Qin ZHANG, Qiang LI, Hong-yan NAN
2017 DEStech Transactions on Environment Energy and Earth Science  
Discontinuous Galerkin methods can overcome the problems of the discretizationand the degree of freedom about standard Galerkin method.  ...  This article summarizes the development and the mathematical model of kinds of discontinuous Galerkin methods.  ...  The New Discontinuous Galerkin Method With the promotion of computing performance and the development of the finite element adaptive method, because of the discontinuous finite element method for solving  ... 
doi:10.12783/dteees/eccsd2016/5836 fatcat:zhylu76lxnel7h7z6ijg6wrnwa

A p-adaptive local discontinuous galerkin level set method for Willmore flow [article]

Ruihan Guo
2016 arXiv   pre-print
In addition, to enhance the efficiency of the proposed LDG scheme and level set method, we employ a p-adaptive local discontinuous Galerkin technique, which applies high order polynomial approximations  ...  In this paper, we present a combination of local discontinuous Galerkin (LDG) method and level set method for simulating Willmore flow.  ...  With the proposed p-adaptive technique, we can improve the efficiency of the local discontinuous Galerkin method for level set equation.  ... 
arXiv:1603.04260v1 fatcat:37x4h3nmurdojhzk33v45i34iy

A p-Adaptive Local Discontinuous Galerkin Level Set Method for Willmore Flow

Ruihan Guo, Francis Filbet
2018 Journal of Scientific Computing  
In addition, to enhance the efficiency of the proposed LDG scheme and level set method, we employ a p-adaptive local discontinuous Galerkin technique, which applies high order polynomial approximations  ...  In this paper, we present a combination of local discontinuous Galerkin (LDG) method and level set method for simulating Willmore flow.  ...  With the proposed p-adaptive technique, we can improve the efficiency of the local discontinuous Galerkin method for level set equation.  ... 
doi:10.1007/s10915-018-0656-3 fatcat:7ytocq7xdffr7hjk52dy7idgba

Page 1380 of Mathematical Reviews Vol. , Issue 2004b [page]

2004 Mathematical Reviews  
The paper deals with a numerical solution of the 2D Dirichlet problem in linear elasticity, based on a discontinuous Galerkin method and on a discontinuous piecewise linear approximation of the displacements  ...  The authors propose a local discontinuous Galerkin method for the numerical approximation of the time-harmonic Maxwell equa- tions in the low-frequency regime.  ... 

ASYMPTOTIC PROFILES WITH FINITE MASS IN ONE-DIMENSIONAL CONTAMINANT TRANSPORT THROUGH POROUS MEDIA: THE FAST REACTION CASE

R. E. GRUNDY, C. J. VAN DUIJN, C. N. DAWSON
1994 Quarterly Journal of Mechanics and Applied Mathematics  
Liu, R., Wheeler, M.F., Dawson, C.N. and Dean, R.H., "On a coupled discontinuous/continuous Galerkin framework and an adaptive penalty scheme for poroelasticity problems,"Computer Methods in Applied Mechanics  ...  Mirabito, C., Dawson, C., Kubatko, E.J., Westerink, J.J. and Bunya, S., "Implementation of a discontinuous Galerkin morphological model on two-dimensional unstructured meshes," Computer Methods in Applied  ... 
doi:10.1093/qjmam/47.1.69 fatcat:clo2eeeymrhztfs3umme6qnr6q

Frontmatter

2016 Computational Methods in Applied Mathematics  
The highly selective international mathematical journal Computational Methods in Applied Mathematics (CMAM) considers original mathematical contributions to computational methods and numerical analysis  ...  409 Xiaobing Feng, Peipei Lu, Xuejun Xu A Hybridizable Discontinuous Galerkin Method for the Time-Harmonic Maxwell Equations with High Wave Number 429 Helmut Harbrecht, Reinhold Schneider A  ...  Voigt An Adaptive Finite Element Multi-Mesh Approach for Interacting Deformable Objects in Flow 475 Volker Schulz, Martin Siebenborn Computational Comparison of Surface Metrics for PDE Constrained  ... 
doi:10.1515/cmam-2016-frontmatter3 fatcat:ll7jqcveq5h3vel2snex7hjery

Galerkin radiosity

Harold R. Zatz
1993 Proceedings of the 20th annual conference on Computer graphics and interactive techniques - SIGGRAPH '93  
The technique is demonstrated on traditional radiosity scenes, as well as environments with untessellated curved surfaces.  ...  Using the Galerkin integral equation technique as a mathematical foundation, surface radiance functions are approximated by polynomials.  ...  Acknowledgements The Program of Computer Graphics at Cornell is one of five sites of the NSF/DARPA Science and Technology Center for Computer Graphics and Scientific Visualization (Grant # ASC-8920219)  ... 
doi:10.1145/166117.166145 dblp:conf/siggraph/Zatz93 fatcat:tl5dcovkznao3py75p3ser77tm

Space-Time Discontinuous Galerkin Method for Large Amplitude Nonlinear Water Waves [chapter]

Yan Xu, Jaap J.W van der Vegt
2009 Computational Fluid Dynamics 2006  
A space-time discontinuous Galerkin (DG) finite element method for nonlinear water waves in an inviscid and incompressible fluid is presented.  ...  The space-time DG method results in a conservative numerical discretization on time dependent deforming meshes which follow the free surface evolution.  ...  This approach combines the benefits of discontinuous Galerkin methods, for instance their suitability for hp-mesh adaptation and parallel computing, with an accurate representation of the time-dependent  ... 
doi:10.1007/978-3-540-92779-2_5 fatcat:37wiyp4pzjhpdhbjmjiaokuvlq

Applications of Discontinuous Galerkin Finite Element Method in Thermomechanical Coupling Problems with Imperfect Thermal Contact

Donghuan Liu, Yinghua Liu
2013 Mathematical Problems in Engineering  
Galerkin finite element method does.  ...  Thermomechanical coupling problems with imperfect thermal contact are analyzed in the present paper with discontinuous Galerkin finite element method.  ...  Although the original impetus of most researches on the discontinuous Galerkin method was the solution of hyperbolic and parabolic problems, the applications of the discontinuous Galerkin method have also  ... 
doi:10.1155/2013/861417 fatcat:c5xcrawhbbamjj4vzy54nxz2ti

A Semi-discrete SUPG Method for Contaminant Transport in Shallow Water Models

Faranak Behzadi, James Charles Newman III
2016 Procedia Computer Science  
In the present paper, a finite element model is developed based on a semi-discrete Streamline Upwind Petrov-Galerkin method to solve the fully-coupled two-dimensional shallow water and contaminant transport  ...  equations on a non-flat bed.  ...  Both the standard Continuous Galerkin (CG) and the Discontinuous Galerkin (DG) methods have been employed to solve the shallow water equations. Bunya et al.  ... 
doi:10.1016/j.procs.2016.05.476 fatcat:bkomezsnuvhgdor2cjbugvbnde

Implicit method and slope limiter in AHMR procedure for high order discontinuous Galerkin methods for compressible flows

Eric Schall, Nicolas Chauchat
2019 Communications in nonlinear science & numerical simulation  
In this paper the robustness and the performance of adaptive hierarchical mesh refinement (AHMR) for high order Discontinuous Galerkin (DG) finite element method with slope limiting procedure combined  ...  Furthermore the limiting method used in this paper can be generalized to any type of mesh in two dimensions. key words: Non-linear Euler equations, Discontinuous Galerkin finite elements methods (DGFEM  ...  The adaptive mesh refinement is A C C E P T E D M A N U S C R I P T 3 Implicit method and slope limiter in AHMR procedure for high order discontinuous Galerkin methods for compressible flows based on a  ... 
doi:10.1016/j.cnsns.2018.12.020 fatcat:l673ohjbb5c47pr7voh5swp5qy

Modeling Evolving Discontinuities with Spacetime Discontinuous Galerkin Methods [chapter]

Reza Abedi, Shuo-Heng Chung, Morgan A. Hawker, Jayandran Palaniappan, Robert B. Haber
2007 IUTAM Bookseries  
We review recent progress in applying spacetime discontinuous Galerkin (SDG) finite element methods to problems whose solutions exhibit various types of moving discontinuities.  ...  Specifically, we show how h-adaptive spacetime meshing can be used to capture weak shocks in linear elastodynamics, how the SDG framework provides a convenient setting for implementing cohesive models  ...  Spacetime Discontinuous Galerkin Methods This contribution reviews recent progress in the use of adaptive spacetime discontinuous Galerkin (SDG) finite element methods for tracking evolving discontinuities  ... 
doi:10.1007/978-1-4020-6530-9_4 fatcat:lad743a3y5b4ddqvaphvrf7pxe

DORiE: A Discontinuous Galerkin Solver for Soil Water Flow and Passive Solute Transport Based on DUNE

Lukas Riedel, Santiago De Ríos, Dion Häfner, Ole Klein
2020 Journal of Open Source Software  
DORiE is a software framework for modelling and simulating transient water flow and passive solute transport in unsaturated porous media with discontinuous Galerkin (DG) methods using the Distributed and  ...  It supports computations with higher-order function spaces on structured and unstructured, non-conforming grids and features advanced numerical routines like flux reconstruction and adaptive grid refinement  ...  Bauser for his constructive comments on this paper. LR was funded by Ministerium für Wissenschaft, Forschung und Kunst Baden-Württemberg (Az 33-7533.-30-20/6/2).  ... 
doi:10.21105/joss.02313 fatcat:jsglfusjhfgcxgfkjt7ntctkcm
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