[HTML][HTML] Gradient flow finite element discretizations with energy-based adaptivity for the Gross-Pitaevskii equation
We present an effective adaptive procedure for the numerical approximation of the steady-
state Gross–Pitaevskii equation. Our approach is solely based on energy minimization, and …
state Gross–Pitaevskii equation. Our approach is solely based on energy minimization, and …
Convergence and quasi-optimal cost of adaptive algorithms for nonlinear operators including iterative linearization and algebraic solver
A Haberl, D Praetorius, S Schimanko… - Numerische Mathematik, 2021 - Springer
We consider a second-order elliptic boundary value problem with strongly monotone and
Lipschitz-continuous nonlinearity. We design and study its adaptive numerical …
Lipschitz-continuous nonlinearity. We design and study its adaptive numerical …
Adaptive iterative linearization Galerkin methods for nonlinear problems
A wide variety of (fixed-point) iterative methods for the solution of nonlinear equations (in
Hilbert spaces) exists. In many cases, such schemes can be interpreted as iterative local …
Hilbert spaces) exists. In many cases, such schemes can be interpreted as iterative local …
On the convergence of adaptive iterative linearized Galerkin methods
A wide variety of different (fixed-point) iterative methods for the solution of nonlinear
equations exists. In this work we will revisit a unified iteration scheme in Hilbert spaces from …
equations exists. In this work we will revisit a unified iteration scheme in Hilbert spaces from …
Guaranteed, locally efficient, and robust a posteriori estimates for nonlinear elliptic problems in iteration-dependent norms. An orthogonal decomposition result based …
K Mitra, M Vohralík - 2023 - inria.hal.science
We consider numerical approximations of nonlinear, monotone, and Lipschitz-continuous
elliptic problems, with gradient-dependent or gradient-independent diffusivity. For this …
elliptic problems, with gradient-dependent or gradient-independent diffusivity. For this …
Stokes flow with Tresca boundary condition: A posteriori error analysis
In this article, a reliable a posteriori error estimate of residual type is derived for a variational
inequality of second kind modeling Stokes equations with Tresca's boundary condition. Two …
inequality of second kind modeling Stokes equations with Tresca's boundary condition. Two …
A numerical energy reduction approach for semilinear diffusion-reaction boundary value problems based on steady-state iterations
We present a novel energy-based numerical analysis of semilinear diffusion-reaction
boundary value problems, where the nonlinear reaction terms need to be neither monotone …
boundary value problems, where the nonlinear reaction terms need to be neither monotone …
An ℎ𝑝-adaptive Newton-discontinuous-Galerkin finite element approach for semilinear elliptic boundary value problems
In this paper we develop an $ hp $-adaptive procedure for the numerical solution of general
second-order semilinear elliptic boundary value problems, with possible singular …
second-order semilinear elliptic boundary value problems, with possible singular …
Discontinuous Galerkin schemes for Stokes flow with Tresca boundary condition: iterative a posteriori error analysis
In two dimensions, we propose and analyse an iterative a posteriori error indicator for the
discontinuous Galerkin finite element approximations of the Stokes equations under …
discontinuous Galerkin finite element approximations of the Stokes equations under …
Stopping criteria for nonlinear variational problems: iterative approach
JD Kamdem, T Sayah - Numerical Algorithms, 2024 - Springer
In this paper, we present and study a stopping criteria based on a priori error estimate for
nonlinear variational problems. We show that for nonlinear variational problems, the a priori …
nonlinear variational problems. We show that for nonlinear variational problems, the a priori …