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math.NA2017

Refined a posteriori error estimation for classical and pressure-robust Stokes finite element methods

P. L. Lederer, C. Merdon, J. Schöberl

Recent works showed that pressure-robust modifications of mixed finite element methods for the Stokes equations outperform their standard versions in many cases. This is achieved b…

math.NA2017★ 26 cited

Convergent tangent plane integrators for the simulation of chiral magnetic skyrmion dynamics

Gino Hrkac, Carl-Martin Pfeiler, Dirk Praetorius +3

We consider the numerical approximation of the Landau-Lifshitz-Gilbert equation, which describes the dynamics of the magnetization in ferromagnetic materials. In addition to the cl…

math.NA2017★ 27 cited

Linear second-order IMEX-type integrator for the (eddy current) Landau-Lifshitz-Gilbert equation

Giovanni Di Fratta, Carl-Martin Pfeiler, Dirk Praetorius +2

Combining ideas from [Alouges et al. (Numer. Math., 128, 2014)] and [Praetorius et al. (Comput. Math. Appl., 2017)], we propose a numerical algorithm for the integration of the non…

math.NA2017

Time-domain boundary integral equation modeling of heat transmission problems

Tianyu Qiu, Alexander Rieder, Francisco-Javier Sayas +1

This paper investigates the numerical modeling of a time-dependent heat transmission problem by the convolution quadrature boundary element method. It introduces the latest theoret…

math.NA2017★ 15 cited

Adaptive vertex-centered finite volume methods for general second-order linear elliptic PDEs

Christoph Erath, Dirk Praetorius

We prove optimal convergence rates for the discretization of a general second-order linear elliptic PDE with an adaptive vertex-centered finite volume scheme. While our prior work…

math.NA2017★ 47 cited

Tensor FEM for spectral fractional diffusion

Lehel Banjai, Jens M. Melenk, Ricardo H. Nochetto +3

We design and analyze several Finite Element Methods (FEMs) applied to the Caffarelli-Silvestre extension that localizes the fractional powers of symmetric, coercive, linear ellipt…