Results 31 to 40 of about 102,481 (112)
Discontinuous Galerkin methods for the biharmonic problem [PDF]
IMA Journal of Numerical Analysis, 2008 This work is concerned with the design and analysis of hp-version discontinuous Galerkin (DG) finite element methods for boundary-value problems involving the biharmonic operator. The first part extends the unified approach of Arnold, Brezzi, Cockburn & Marini (SIAM J. Numer. Anal.
Georgoulis, EH, Houston, P
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Robust Interior Penalty Discontinuous Galerkin Methods
Journal of Scientific Computing, 2022 Classical interior penalty discontinuous Galerkin (IPDG) methods for diffusion problems require a number of assumptions on the local variation of mesh-size, polynomial degree, and of the diffusion coefficient to determine the values of the, so-called, discontinuity-penalization parameter and/or to perform error analysis.
Dong, Zhaonan, Georgoulis, Emmanuil
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Proceedings in Applied Mathematics and Mechanics, Volume 26, Issue 4, December 2026.ABSTRACT Stochastic Galerkin methods offer unexplored potential for the numerical simulation of parabolic problems with random variables, in particular if they are combined with variational discretizations of the space and time variables. Due to the high dimensionality, the solution of the arising algebraic systems do not become feasible without ...
Moataz Dawor +2 more
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Computer Methods in Applied Mechanics and Engineering, 2018 We propose and analyze a high-order Discontinuous Galerkin Finite Element Method for the approximate solution of wave propagation problems modeled by the elastodynamics equations on computational meshes made by polygonal and polyhedral elements.
P. Antonietti, I. Mazzieri
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International Journal for Numerical Methods in Fluids, Volume 98, Issue 10, Page 1143-1164, October 2026.This article provides important geometric formulas for node‐centered, edge‐based schemes in any number of dimensions. These formulas are noteworthy, as they do not require the explicit formation of dual regions. We prove several key geometric results, with a particular focus on the four‐dimensional case, due to potential space‐time applications ...
Nicholas Tufillaro +2 more
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Weight-Adjusted Discontinuous Galerkin Methods: Curvilinear Meshes [PDF]
SIAM Journal on Scientific Computing, 2016 Traditional time-domain discontinuous Galerkin (DG) methods result in large storage costs at high orders of approximation due to the storage of dense elemental matrices.
J. Chan, Russell J. Hewett, T. Warburton
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Multiphysics Simulation of Positive Streamer Discharge in Air Using Finite Element Method
International Journal for Numerical Methods in Engineering, Volume 127, Issue 18, 30 September 2026.ABSTRACT Streamer discharge modeling by means of the Finite Element Method (FEM) presents a formidable challenge in computational physics due to its nonlinear and convection‐dominated characteristics that cause numerical instabilities, including negative densities of charged particles.
Hasupama Jayasinghe +3 more
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Adaptive discontinuous Galerkin methods for elliptic interface problems
Mathematics of Computation, 2017 An interior-penalty discontinuous Galerkin (dG) method for an elliptic interface problem involving, possibly, curved interfaces, with flux-balancing interface conditions, e.g., modelling mass transfer of solutes through semipermeable membranes, is ...
A. Cangiani +2 more
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International Journal for Numerical Methods in Engineering, Volume 127, Issue 17, 15 September 2026.ABSTRACT In this contribution, we focus on the Reynolds‐averaged Navier‐Stokes (RANS) models and their exploitation to build reliable reduced‐order models to further accelerate predictions for real‐time applications and many‐query scenarios. Specifically, we investigate how machine learning can be employed to enhance the predictive capabilities of the ...
Davide Oberto +2 more
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Analysis of Mixed Interior Penalty Discontinuous Galerkin Methods for the Cahn-Hilliard Equation and the Hele-Shaw Flow [PDF]
SIAM Journal on Numerical Analysis, 2015 This paper proposes and analyzes two fully discrete mixed interior penalty discontinuous Galerkin (DG) methods for the fourth order nonlinear Cahn--Hilliard equation. Both methods use the backward Euler method for time discretization and interior penalty
Xiaobing Feng, Yukun Li, Y. Xing
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