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pro vyhledávání: '"Linders, Viktor"'
A stencil-adaptive SBP-SAT finite difference scheme is shown to display superconvergent behavior. Applied to the linear advection equation, it has a convergence rate $\mathcal{O}(\Delta x^4)$ in contrast to a conventional scheme, which converges at a
Externí odkaz:
http://arxiv.org/abs/2307.14034
Publikováno v:
Bit Numer Math 63, 45 (2023)
We consider entropy conservative and dissipative discretizations of nonlinear conservation laws with implicit time discretizations and investigate the influence of iterative methods used to solve the arising nonlinear equations. We show that Newton's
Externí odkaz:
http://arxiv.org/abs/2302.13579
Autor:
Linders, Viktor, Birken, Philipp
Publikováno v:
SIAM Journal on Scientific Computing, 2024
Conservation and consistency are fundamental properties of discretizations of systems of hyperbolic conservation laws. Here, these concepts are extended to the realm of iterative methods by formally defining locally conservative and flux consistent i
Externí odkaz:
http://arxiv.org/abs/2206.10943
We discuss two approaches for the formulation and implementation of space-time discontinuous Galerkin spectral element methods (DG-SEM). In one, time is treated as an additional coordinate direction and a Galerkin procedure is applied to the entire p
Externí odkaz:
http://arxiv.org/abs/2201.05800
Autor:
Linders, Viktor
Summation-By-Parts (SBP) methods provide a systematic way of constructing provably stable numerical schemes. However, many proofs of convergence and accuracy rely on the assumption that the SBP operator possesses a particular eigenvalue property. In
Externí odkaz:
http://arxiv.org/abs/2201.01193
Local Fourier Analysis of a Space-Time Multigrid Method for DG-SEM for the Linear Advection Equation
In this paper we present a Local Fourier Analysis of a space-time multigrid solver for a hyperbolic test problem. The space-time discretization is based on arbitrarily high order discontinuous Galerkin spectral element methods in time and a first ord
Externí odkaz:
http://arxiv.org/abs/2112.03115
Autor:
Birken, Philipp, Linders, Viktor
Conservation properties of iterative methods applied to implicit finite volume discretizations of nonlinear conservation laws are analyzed. It is shown that any consistent multistep or Runge-Kutta method is globally conservative. Further, it is shown
Externí odkaz:
http://arxiv.org/abs/2106.10088
Autor:
Linders, Viktor
In this thesis we consider errors arising from finite difference operators on summation-by-parts (SBP) form, used in the discretisation of partial differential equations. The SBP operators are augmented with simultaneous-approximation-terms (SATs) to
Externí odkaz:
http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-143059
Publikováno v:
In Journal of Computational Physics 15 October 2020 419
Publikováno v:
In Journal of Computational Physics 1 June 2020 410