Zobrazeno 1 - 10
of 65
pro vyhledávání: '"Heid, Pascal"'
Publikováno v:
Comptes Rendus. Mécanique, Vol , Iss , Pp 1-25 (2022)
We consider a system of nonlinear partial differential equations modelling steady flow of an incompressible chemically reacting non-Newtonian fluid, whose viscosity depends on both the shear-rate and the concentration; in particular, the viscosity is
Externí odkaz:
https://doaj.org/article/0573c2f41b5543c587df41a6d2269208
The challenge of approximating functions in infinite-dimensional spaces from finite samples is widely regarded as formidable. We delve into the challenging problem of the numerical approximation of Sobolev-smooth functions defined on probability spac
Externí odkaz:
http://arxiv.org/abs/2310.19548
Autor:
Heid, Pascal
The focus of the present work is the (theoretical) approximation of a solution of the p(x)-Poisson equation. To devise an iterative solver with guaranteed convergence, we will consider a relaxation of the original problem in terms of a truncation of
Externí odkaz:
http://arxiv.org/abs/2304.01566
Autor:
Brunner, Maximilian, Heid, Pascal, Innerberger, Michael, Miraçi, Ani, Praetorius, Dirk, Streitberger, Julian
We consider a general nonsymmetric second-order linear elliptic PDE in the framework of the Lax-Milgram lemma. We formulate and analyze an adaptive finite element algorithm with arbitrary polynomial degree that steers the adaptive mesh-refinement and
Externí odkaz:
http://arxiv.org/abs/2212.00353
Autor:
Heid, Pascal
We will consider the damped Newton method for strongly monotone and Lipschitz continuous operator equations in a variational setting. We will provide a very accessible justification why the undamped Newton method performs better than its damped count
Externí odkaz:
http://arxiv.org/abs/2210.17107
We present a novel energy-based numerical analysis of semilinear diffusion-reaction boundary value problems. Based on a suitable variational setting, the proposed computational scheme can be seen as an energy minimisation approach. More specifically,
Externí odkaz:
http://arxiv.org/abs/2202.07398
Autor:
Heid, Pascal
We will make a link between the steepest descent method for an unconstrained minimisation problem and fixed-point iterations for its Euler-Lagrange equation. In this context, we shall rediscover the preconditioned nonlinear conjugate gradient method
Externí odkaz:
http://arxiv.org/abs/2109.09108
Autor:
Heid, Pascal, Süli, Endre
In this work, we introduce an iterative linearised finite element method for the solution of Bingham fluid flow problems. The proposed algorithm has the favourable property that a subsequence of the sequence of iterates generated converges weakly to
Externí odkaz:
http://arxiv.org/abs/2109.05991
Autor:
Heid, Pascal, Wihler, Thomas P.
The classical Ka\v{c}anov scheme for the solution of nonlinear variational problems can be interpreted as a fixed point iteration method that updates a given approximation by solving a linear problem in each step. Based on this observation, we introd
Externí odkaz:
http://arxiv.org/abs/2101.10137
Autor:
Heid, Pascal, Süli, Endre
We explore the convergence rate of the Ka\v{c}anov iteration scheme for different models of shear-thinning fluids, including Carreau and power-law type explicit quasi-Newtonian constitutive laws. It is shown that the energy difference contracts along
Externí odkaz:
http://arxiv.org/abs/2101.01398