Convergence analysis of the scaled boundary finite element method for the Laplace equation

05/05/2020
by   Fleurianne Bertrand, et al.
0

The scaled boundary finite element method (SBFEM) is a relatively recent boundary element method that allows the approximation of solutions to PDEs without the need of a fundamental solution. A theoretical framework for the convergence analysis of SBFEM is proposed here. This is achieved by defining a space of semi-discrete functions and constructing an interpolation operator onto this space. We prove error estimates for this interpolation operator and show that optimal convergence to the solution can be obtained in SBFEM. These theoretical results are backed by a numerical example.

READ FULL TEXT
POST COMMENT

Comments

There are no comments yet.

Authors

page 1

page 2

page 3

page 4

11/11/2020

Finite element method on a Bakhvalov-type mesh for a singularly perturbed problem with two parameters

We reconsider a linear finite element method on a Bakhvalov-type mesh fo...
12/24/2020

Error estimates for the Scaled Boundary Finite Element Method

The Scaled Boundary Finite Element Method (SBFEM) is a technique in whic...
07/17/2020

Non-symmetric isogeometric FEM-BEM couplings

We present a coupling of the Finite Element and the Boundary Element Met...
07/10/2021

On the coupling of the Curved Virtual Element Method with the one-equation Boundary Element Method for 2D exterior Helmholtz problems

We consider the Helmholtz equation defined in unbounded domains, externa...
12/15/2021

Interpolation Operator on negative Sobolev Spaces

We introduce a Scott–Zhang type projection operator mapping to Lagrange ...
07/04/2019

Analysis and numerical simulation of the nonlinear beam equation with moving ends

The numerical analysis for the small amplitude motion of an elastic beam...
07/05/2021

Mathematical foundations of adaptive isogeometric analysis

This paper reviews the state of the art and discusses recent development...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.