# Convergence & Extrapolation for Practising Engineers

## Introduction

The idea that with mesh refinement a finite element model should converge to the appropriate theoretical mathematical model is one on which engineers rely. The theoretical notions of convergence are though not necessarily simple to grasp and although theoretical rates of convergence can be obtained, these are not always achieved in practical finite element models. This project will look at the nature of convergence using practical engineering examples. Methods for extrapolating from the results of a series of analyses using increasingly refined meshes towards a better approximation of the theoretical solution will be examined. The outcome of this work will be one/two articles which, it is hoped, will be accepted for publication in the NAFEMS Benchmark Magazine.

### Team

Angus Ramsay

Edward Maunder

### Collaboaration

Nick Stevens, Senior Consultant at Tor Engineering is working with RMA on this project.

Łukasz Skotny, Assistant Professor at Wroclaw University of Technology and Owner of Enterfea is working with RMA on this project.

Len Schwer, of Schwer Engineering & Consulting Services has a long standing interest and expertise in Verification & Validation (V&V). Len has generously offered to act as a reviewer for this project.

### Useful Links

Blog: Correct Mesh Size - A Quick Guide

Blog: Richardson Extrapolation and Grid Convergence Index

Glossary: Convergence

Article: “Is Your Mesh Refined Enough? Estimating Discretization Error Using CGI”