Dubuis, Samuel Picasso, Marco Wittwer, Peter
Published in
Computational Methods in Applied Mathematics

A space-time adaptive algorithm to solve the motion of a rigid disk in an incompressible Newtonian fluid is presented, which allows collision or quasi-collision processes to be computed with high accuracy. In particular, we recover the theoretical result proven in [M. Hillairet, Lack of collision between solid bodies in a 2D incompressible viscous ...

Giani, Stefano Grubišić, Luka Heltai, Luca Mulita, Ornela
Published in
Computational Methods in Applied Mathematics

We present a perturbed subspace iteration algorithm to approximate the lowermost eigenvalue cluster of an elliptic eigenvalue problem. As a prototype, we consider the Laplace eigenvalue problem posed in a polygonal domain. The algorithm is motivated by the analysis of inexact (perturbed) inverse iteration algorithms in numerical linear algebra. We ...

Praetorius, Dirk Repin, Sergey Sauter, Stefan A.
Published in
Computational Methods in Applied Mathematics

Heid, Pascal Praetorius, Dirk Wihler, Thomas P.
Published in
Computational Methods in Applied Mathematics

We revisit a unified methodology for the iterative solution of nonlinear equations in Hilbert spaces. Our key observation is that the general approach from [P. Heid and T. P. Wihler, Adaptive iterative linearization Galerkin methods for nonlinear problems, Math. Comp. 89 2020, 326, 2707–2734; P. Heid and T. P. Wihler, On the convergence of adaptive...

Carstensen, Carsten Nataraj, Neela
Published in
Computational Methods in Applied Mathematics

This article on nonconforming schemes for m harmonic problems simultaneously treats the Crouzeix–Raviart ( m = 1 {m=1} ) and the Morley finite elements ( m = 2 {m=2} ) for the original and for modified right-hand side F in the dual space V * := H - m ( Ω ) {V^{*}:=H^{-m}(\Omega)} to the energy space V := H 0 m ( Ω ) {V:=H^{m}_{0}(\Omega)} . The...

Miraçi, Ani Papež, Jan Vohralík, Martin
Published in
Computational Methods in Applied Mathematics

In this work, we study a local adaptive smoothing algorithm for a-posteriori-steered p-robust multigrid methods. The solver tackles a linear system which is generated by the discretization of a second-order elliptic diffusion problem using conforming finite elements of polynomial order p ≥ 1 {p\geq 1} . After one V-cycle (“full-smoothing” substep) ...

Endtmayer, Bernhard Langer, Ulrich Wick, Thomas
Published in
Computational Methods in Applied Mathematics

We derive efficient and reliable goal-oriented error estimations, and devise adaptive mesh procedures for the finite element method that are based on the localization of a posteriori estimates. In our previous work [B. Endtmayer, U. Langer and T. Wick, Two-side a posteriori error estimates for the dual-weighted residual method, SIAM J. Sci. Comput....

Maity, Ruma Rani Majumdar, Apala Nataraj, Neela
Published in
Computational Methods in Applied Mathematics

We study a system of semi-linear elliptic partial differential equations with a lower order cubic nonlinear term, and inhomogeneous Dirichlet boundary conditions, relevant for two-dimensional bistable liquid crystal devices, within a reduced Landau–de Gennes framework. The main results are (i) a priori error estimates for the energy norm, within th...

Egger, Herbert Habrich, Oliver Shashkov, Vsevolod
Published in
Computational Methods in Applied Mathematics

A general framework for the numerical approximation of evolution problems is presented that allows to preserve an underlying dissipative Hamiltonian or gradient structure exactly. The approach relies on rewriting the evolution problem in a particular form that complies with the underlying geometric structure. The Galerkin approximation of a corresp...

Stevenson, Rob van Venetië, Raymond
Published in
Computational Methods in Applied Mathematics

We propose a multi-level type operator that can be used in the framework of operator (or Caldéron) preconditioning to construct uniform preconditioners for negative order operators discretized by piecewise polynomials on a family of possibly locally refined partitions. The cost of applying this multi-level operator scales linearly in the number of ...