Auxiliary Space Preconditioning of Finite Element Equations Using a Nonconforming Interior Penalty Reformulation and Static Condensation

10/15/2019
by   Delyan Z. Kalchev, et al.
0

We modify the well-known interior penalty finite element discretization method so that it allows for element-by-element assembly. This is possible due to the introduction of additional unknowns associated with the interfaces between neighboring elements.The resulting bilinear form, and a Schur complement (reduced) version of it, are utilized in a number of auxiliary space preconditioners for the original conforming finite element discretization problem. These preconditioners are analyzed and their performance is illustrated on model second order scalar elliptic problems discretized with high order elements.

READ FULL TEXT

page 3

page 4

page 18

research
12/10/2019

A Condensed Constrained Nonconforming Mortar-based Approach for Preconditioning Finite Element Discretization Problems

This paper presents and studies an approach for constructing auxiliary s...
research
10/10/2019

P_1–nonconforming polyhedral finite elements in high dimensions

We consider the lowest–degree nonconforming finite element methods for t...
research
06/20/2022

Finite Element de Rham and Stokes Complexes in Three Dimensions

Finite element de Rham complexes and finite element Stokes complexes wit...
research
02/18/2022

Analysis of optimal preconditioners for CutFEM

In this paper we consider a class of unfitted finite element methods for...
research
11/07/2017

Exposing and exploiting structure: optimal code generation for high-order finite element methods

Code generation based software platforms, such as Firedrake, have become...
research
07/27/2021

Stability for finite element discretization of some elliptic inverse parameter problems from internal data – application to elastography

In this article, we provide stability estimates for the finite element d...
research
09/28/2020

Microstructure-informed reduced modes synthesized with Wang tiles and the Generalized Finite Element Method

A recently introduced representation by a set of Wang tiles – a generali...

Please sign up or login with your details

Forgot password? Click here to reset