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Related papers: Symmetric coupling of LDG-FEM and DG-BEM

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We present a coupling of the Finite Element and the Boundary Element Method in an isogeometric framework to approximate either two-dimensional Laplace interface problems or boundary value problems consisting in two disjoint domains. We…

Numerical Analysis · Mathematics 2020-07-24 Mehdi Elasmi , Christoph Erath , Stefan Kurz

We propose an unfitted interface penalty Discontinuous Galerkin-Finite Element Method (UIPDG-FEM) for elliptic interface problems. This hybrid method combines the interior penalty discontinuous Galerkin (IPDG) terms near the…

Numerical Analysis · Mathematics 2025-05-27 Juan Han , Haijun Wu , Yuanming Xiao

We consider the symmetric FEM-BEM coupling that connects two linear elliptic second order partial differential equations posed in a bounded domain $\Omega$ and its complement, where the exterior problem is restated by an integral equation…

Numerical Analysis · Mathematics 2017-01-30 Jens Markus Melenk , Dirk Praetorius , Barbara Wohlmuth

This work focuses on a class of elliptic boundary value problems with diffusive, advective and reactive terms, motivated by the study of three-dimensional heterogeneous physical systems composed of two or more media separated by a selective…

Numerical Analysis · Mathematics 2018-04-20 Riccardo Sacco , Aurelio Giancarlo Mauri , Giovanna Guidoboni

Many problems in electrical engineering or fluid mechanics can be modeled by parabolic-elliptic interface problems, where the domain for the exterior elliptic problem might be unbounded. A possibility to solve this class of problems…

Numerical Analysis · Mathematics 2018-05-15 Christoph Erath , Robert Schorr

In this paper a discretization based on discontinuous Galerkin (DG) method for an elliptic two-dimensional problem with discontinuous coefficients is considered. The problem is posed on a polygonal region $\Omega$ which is a union of $N$…

Numerical Analysis · Mathematics 2014-01-07 Maksymilian Dryja , Juan Galvis , Marcus Sarkis

We consider a system of second order non-linear elliptic partial differential equations that models the equilibrium configurations of a two dimensional planar bistable nematic liquid crystal device. Discontinuous Galerkin finite element…

Numerical Analysis · Mathematics 2020-05-29 Ruma Rani Maity , Apala Majumdar , Neela Nataraj

In "I. Smears, E. S\"{u}li, \emph{Discontinuous Galerkin finite element approximation of nondivergence form elliptic equations with Cord\'{e}s coefficients. SIAM J. Numer Anal., 51(4):2088-2106, 2013}" the authors designed and analysed a…

Numerical Analysis · Mathematics 2018-02-19 Ellya Kawecki

We propose a discontinuous Galerkin(DG) method to approximate the elliptic interface problem on unfitted mesh using a new approximation space. The approximation space is constructed by patch reconstruction with one degree of freedom per…

Numerical Analysis · Mathematics 2020-12-10 Ruo Li , Fanyi Yang

This work studies discontinuous Galerkin (DG) approximations of the boundary value problem for homogeneous transversely isotropic linear elastic bodies. Low-order approximations on triangles are adopted, with the use of three interior…

Analysis of PDEs · Mathematics 2019-11-26 B. J. Grieshaber , F. Rasolofoson , B. D. Reddy

We consider the initial/boundary value problem for a diffusion equation involving multiple time-fractional derivatives on a bounded convex polyhedral domain. We analyze a space semidiscrete scheme based on the standard Galerkin finite…

Numerical Analysis · Mathematics 2015-06-18 Bangti Jin , Raytcho Lazarov , Yikan Liu , Zhi Zhou

We propose an $hp$-adaptive discontinuous Galerkin finite element method (DGFEM) to approximate the solution of a static crack boundary value problem. The mathematical model describes the behavior of a geometrically linear strain-limiting…

Numerical Analysis · Mathematics 2024-11-04 Ram Manohar , S. M. Mallikarjunaiah

We present a wavenumber-explicit analysis of FEM-BEM coupling methods for time-harmonic Helmholtz problems proposed in arXiv:2004.03523 for conforming discretizations and in arXiv:2105.06173 for discontinuous Galerkin (DG) volume…

Numerical Analysis · Mathematics 2024-07-08 Jens Markus Melenk , Ilaria Perugia , Alexander Rieder

We derive and analyze a symmetric interior penalty discontinuous Galerkin scheme for the approximation of the second-order form of the radiative transfer equation in slab geometry. Using appropriate trace lemmas, the analysis can be carried…

Numerical Analysis · Mathematics 2023-12-20 Riccardo Bardin , Fleurianne Bertrand , Olena Palii , Matthias Schlottbom

We present a new line-based discontinuous Galerkin (DG) discretization scheme for first- and second-order systems of partial differential equations. The scheme is based on fully unstructured meshes of quadrilateral or hexahedral elements,…

Numerical Analysis · Mathematics 2015-06-04 Per-Olof Persson

We design and analyze a coupling of a discontinuous Galerkin finite element method with a boundary element method to solve the Helmholtz equation with variable coefficients in three dimensions. The coupling is realized with a mortar…

Numerical Analysis · Mathematics 2024-07-25 Christoph Erath , Lorenzo Mascotto , Jens Markus Melenk , Ilaria Perugia , Alexander Rieder

We present and analyze a discontinuous variant of the hp-version of the boundary element Galerkin method with quasi-uniform meshes. The model problem is that of the hypersingular integral operator on an (open or closed) polyhedral surface.…

Numerical Analysis · Mathematics 2012-06-28 Norbert Heuer , Salim Meddahi

We combine continuous and discontinuous Galerkin methods in the setting of a model diffusion problem. Starting from a hybrid discontinuous formulation, we replace element interiors by more general subsets of the computational domain -…

Computational Physics · Physics 2018-11-30 Martin Vymazal , David Moxey , Chris Cantwell , Spencer Sherwin , Robert M. Kirby

We consider singularly perturbed boundary value problems with a simple interior turning point whose solutions exhibit an interior layer. These problems are discretised using higher order finite elements on layer-adapted piecewise…

Numerical Analysis · Mathematics 2017-09-29 Simon Becher

In this paper we study the finite element approximation of systems of second-order nonlinear hyperbolic equations. The proposed numerical method combines a $hp$-version discontinuous Galerkin finite element approximation in the time…

Numerical Analysis · Mathematics 2022-12-02 Aili Shao