Showing 2018 · math.NAShow all

20 papers · 2 filters

math.NA2018★ 3 cited

Adaptive Uzawa algorithm for the Stokes equation

Giovanni Di Fratta, Thomas Führer, Gregor Gantner +1

Based on the Uzawa algorithm, we consider an adaptive finite element method for the Stokes system. We prove linear convergence with optimal algebraic rates for the residual estimat…

math.NA2018★ 22 cited

Convergence of adaptive stochastic Galerkin FEM

Alex Bespalov, Dirk Praetorius, Leonardo Rocchi +1

We propose and analyze novel adaptive algorithms for the numerical solution of elliptic partial differential equations with parametric uncertainty. Four different marking strategie…

math.NA2018★ 5 cited

Stable decompositions of -BEM spaces and an optimal Schwarz preconditioner for the hypersingular integral operator in 3D

Michael Karkulik, Jens Markus Melenk, Alexander Rieder

We consider fractional Sobolev spaces , , on a 2D surface . We show that functions in can be decomposed into contributions with local support in a s…

math.NA2018

Tight Continuous-Time Reachtubes for Lagrangian Reachability

Jacek Cyranka, Md. Ariful Islam, Scott A. Smolka +2

We introduce continuous Lagrangian reachability (CLRT), a new algorithm for the computation of a tight and continuous-time reachtube for the solution flows of a nonlinear, time-var…

math.NA2018★ 1 cited

Convergence of an implicit Euler Galerkin scheme for Poisson-Maxwell-Stefan systems

Ansgar Jüngel, Oliver Leingang

A fully discrete Galerkin scheme for a thermodynamically consistent transient Max-well-Stefan system for the mass particle densities, coupled to the Poisson equation for the electr…

math.NA2018★ 13 cited

Computable upper error bounds for Krylov approximations to matrix exponentials and associated -functions

Tobias Jawecki, Winfried Auzinger, Othmar Koch

An a posteriori estimate for the error of a standard Krylov approximation to the matrix exponential is derived. The estimate is based on the defect (residual) of the Krylov approxi…