Results 51 to 60 of about 1,001 (186)

-Error Estimates of the Extrapolated Crank-Nicolson Discontinuous Galerkin Approximations for Nonlinear Sobolev Equations

Journal of Inequalities and Applications, 2010
We analyze discontinuous Galerkin methods with penalty terms, namely, symmetric interior penalty Galerkin methods, to solve nonlinear Sobolev equations.
Lee HyunYoung, Shin JunYong, Ohm MiRay
doaj  

Comparison of DDFV and DG Methods for Flow in Anisotropic Heterogeneous Porous Media

Oil & Gas Science and Technology, 2014
We present a preliminary work to simulate gas injection in deep aquifers. Unsteady single-phase flows are considered. We compare Discrete Duality Finite Volume (DDFV, Discrete Duality Finite Volume) and Discontinuous Galerkin (DG, Discontinuous Galerkin)
Baron V., Coudière Y., Sochala P.
doaj   +1 more source

Totally Volume Integral of Fluxes for Discontinuous Galerkin Method (TVI-DG) I-Unsteady Scalar One Dimensional Conservation Laws

مجلة المختار للعلوم, 2017
The volume integral of Riemann flux in the discontinuous Galerkin (DG) method is introduced in this paper. The boundaries integrals of the fluxes (Riemann flux) are transformed into volume integral.
Ibrahim. M. Rustum, ElHadi. I. Elhadi
doaj   +1 more source

Homogenization With Guaranteed Bounds via Primal‐Dual Physically Informed Neural Networks

International Journal for Numerical Methods in Engineering, Volume 127, Issue 6, 30 March 2026.
ABSTRACT Physics‐informed neural networks (PINNs) have shown promise in solving partial differential equations (PDEs) relevant to multiscale modeling, but they often fail when applied to materials with discontinuous coefficients, such as media with piecewise constant properties. This paper introduces a dual formulation for the PINN framework to improve
Liya Gaynutdinova, Ondřej Rokoš, Martin Doškář, Ivana Pultarová   +3 more
wiley   +1 more source

Distributional derivatives and stability of discontinuous Galerkin finite element approximation methods

Electronic Journal of Differential Equations, 2016
The goal of this article is to explore and motivate stabilization requirements for various types of discontinuous Galerkin (DG) methods. A new approach for the understanding of DG approximation methods for second order elliptic partial differential ...
Thomas Lewis
doaj  

Discontinuous Galerkin method on reference domain

Computer Assisted Methods in Engineering and Science, 2017
A reference domain is chosen to formulate numerical model using the discontinuous Galerkin with finite difference (DGFD) method. The differential problem, which is defined for the real domain, is transformed in a weak form to the reference domain.
Jan Jaśkowiec
doaj   +1 more source

Generalized Multiscale Finite Element Method for Elastic Wave Propagation in the Frequency Domain

Computation, 2020
In this work, we consider elastic wave propagation in fractured media. The mathematical model is described by the Helmholtz problem related to wave propagation with specific interface conditions (Linear Slip Model, LSM) on the fracture in the frequency ...
Uygulana Gavrilieva, Maria Vasilyeva, Eric T. Chung   +2 more
doaj   +1 more source

Penalty‐free discontinuous Galerkin method

International Journal for Numerical Methods in Engineering
AbstractIn this article, we present a new high‐order discontinuous Galerkin (DG) method, in which neither a penalty parameter nor a stabilization parameter is needed. We refer to this method as penalty‐free DG. In this method, the trial and test functions belong to the broken Sobolev space, in which the functions are in general discontinuous on the ...
Jan Jaśkowiec, N. Sukumar
openaire   +2 more sources

Towards adaptive discontinuous Petrov‐Galerkin methods [PDF]

PAMM, 2016
AbstractThe discontinuous Petrov‐Galerkin (dPG) method is a minimum residual method with broken test functions for instant stability. The methodology is written in an abstract framework with product spaces. It is applied to the Poisson model problem, the Stokes equation, and linear elasticity with low‐order discretizations.
Bringmann, P., Carstensen, C., Gallistl, D., Hellwig, F., Peterseim, D., Puttkammer, S., Rabus, H., Storn, Johannes   +7 more
openaire   +2 more sources

Application of Discontinuity Layout Optimization to Metal Shells and Assemblies

International Journal for Numerical Methods in Engineering, Volume 127, Issue 5, 15 March 2026.
ABSTRACT Discontinuity Layout Optimization (DLO) provides a computationally efficient means of determining collapse loads and associated failure mechanisms across a wide spectrum of plasticity problems. The classical DLO method has focused separately on in‐plane and out‐of‐plane plasticity.
John Valentino, Linwei He, Matthew Gilbert   +2 more
wiley   +1 more source