
A family of C^1 quadrilateral finite elements
We present a novel family of C^1 quadrilateral finite elements, which de...
read it

Simple curlcurlconforming finite elements in two dimensions
We construct smooth finite element de Rham complexes in two space dimens...
read it

A scalable and robust preconditioner for highorder FEM based on the fast diagonalization method
Pavarino proved that the additive Schwarz method with vertex patches and...
read it

A family of finite element Stokes complexes in three dimensions
We construct finite element Stokes complexes on tetrahedral meshes in th...
read it

A domain decomposition method for Isogeometric multipatch problems with inexact local solvers
In Isogeometric Analysis, the computational domain is often described as...
read it

Tensor BSpline Numerical Methods for PDEs: a HighPerformance Alternative to FEM
Tensor Bspline methods are a highperformance alternative to solve part...
read it

Full waveform inversion using triangular waveform adapted meshes
In this article, continuous Galerkin finite elements are applied to perf...
read it
Additive Schwarz methods for serendipity elements
While solving Partial Differential Equations (PDEs) with finite element methods (FEM), serendipity elements allow us to obtain the same order of accuracy as rectangular tensorproduct elements with many fewer degrees of freedom (DOFs). To realize the possible computational savings, we develop some additive Schwarz methods (ASM) based on solving local patch problems. Adapting arguments from Pavarino for the tensorproduct case, we prove that patch smoothers give conditioning estimates independent of the polynomial degree for a model problem. We also combine this with a loworder global operator to give an optimal twogrid method, with conditioning estimates independent of the mesh size and polynomial degree. The theory holds for serendipity elements in two and three dimensions, and can be extended to full multigrid algorithms. Numerical experiments using Firedrake and PETSc confirm this theory and demonstrate efficiency relative to standard elements.
READ FULL TEXT
Comments
There are no comments yet.