Zobrazeno 1 - 10
of 25
pro vyhledávání: '"Philipp Öffner"'
Publikováno v:
SIAM Journal on Numerical Analysis. 61:733-754
Summation-by-parts (SBP) operators are popular building blocks for systematically developing stable and high-order accurate numerical methods for time-dependent differential equations. The main idea behind existing SBP operators is that the solution
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::4311c476d469435b72eeb5d70b95bb50
https://doi.org/10.1137/22m1470141
https://doi.org/10.1137/22m1470141
Publikováno v:
Applied Numerical Mathematics. 182:117-147
Patankar-type schemes are linearly implicit time integration methods designed to be unconditionally positivity-preserving. However, there are only little results on their stability or robustness. We suggest two approaches to analyze the performance a
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::a984c5e2c4a1b3f38d9499b3948f9406
https://doi.org/10.1016/j.apnum.2022.07.014
https://doi.org/10.1016/j.apnum.2022.07.014
The choice of the shape parameter highly effects the behaviour of radial basis function (RBF) approximations, as it needs to be selected to balance between the ill-conditioning of the interpolation matrix and high accuracy. In this paper, we demonstr
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::ef29348f3317ad0d426c975b4b09f018
http://arxiv.org/abs/2210.16945
http://arxiv.org/abs/2210.16945
Publikováno v:
Communications on Applied Mathematics and Computation. 5:573-595
In the hyperbolic research community, there exists the strong belief that a continuous Galerkin scheme is notoriously unstable and additional stabilization terms have to be added to guarantee stability. In the first part of the series [6], the applic
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::92e0b0fd1dde53f712c49212909ca8ca
https://doi.org/10.1007/s42967-020-00086-2
https://doi.org/10.1007/s42967-020-00086-2
Autor:
Philipp Öffner, Davide Torlo
Publikováno v:
Applied Numerical Mathematics. 153:15-34
Production-destruction systems (PDS) of ordinary differential equations (ODEs) are used to describe physical and biological reactions in nature. The considered quantities are subject to natural laws. Therefore, they preserve positivity and conservati
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::a51cf6c0536b1b6a152a0fcdc1332aa6
https://doi.org/10.1016/j.apnum.2020.01.025
https://doi.org/10.1016/j.apnum.2020.01.025
Publikováno v:
Applied Mathematics and Computation
Applied Mathematics and Computation, 2023, 440, pp.127644. ⟨10.1016/j.amc.2022.127644⟩
Applied Mathematics and Computation, 2023, 440, pp.127644. ⟨10.1016/j.amc.2022.127644⟩
International audience; In this paper, we develop a fully discrete entropy preserving ADER-Discontinuous Galerkin (ADER-DG) method. To obtain this desired result, we equip the space part of the method with entropy correction terms that balance the en
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::2523c1cbd786ccab27b5a1106b026976
https://doi.org/10.1016/j.amc.2022.127644
https://doi.org/10.1016/j.amc.2022.127644
Convergence of discontinuous Galerkin schemes for the Euler equations via dissipative weak solutions
Publikováno v:
Applied Mathematics and Computation. 436:127508
In this paper, we present convergence analysis of high-order finite element based methods, in particular, we focus on a discontinuous Galerkin scheme using summation-by-parts operators. To this end, it is crucial that structure preserving properties,
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::fcf111094dc4db8cae6913bee4cfb1f0
https://doi.org/10.1016/j.amc.2022.127508
https://doi.org/10.1016/j.amc.2022.127508
In this work, we investigate (energy) stability of global radial basis function (RBF) methods for linear advection problems. Classically, boundary conditions (BC) are enforced strongly in RBF methods. By now it is well-known that this can lead to sta
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::6a2143ea733053929dc3d5df46edd70d
http://arxiv.org/abs/2101.09623
http://arxiv.org/abs/2101.09623
We present a class of discretisation spaces and H(div)-conformal elements that can be built on any polytope. Bridging the flexibility of the Virtual Element spaces towards the element’s shape with the divergence properties of the Raviart–Thomas e
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::73eb8bac1a54a33c21320ed56b1ce6e2
https://www.zora.uzh.ch/id/eprint/202210/
https://www.zora.uzh.ch/id/eprint/202210/
Autor:
Philipp Öffner
The book focuses on stability and approximation results concerning recent numerical methods for the numerical solution of hyperbolic conservation laws. The work begins with a detailed and thorough introduction of hyperbolic conservation/balance laws