Tutorials

Table of Contents

• Hierarchical approximation
• Hello world
• The Poisson equation and difussion problems
• Solid elasticity problems
• Nonlinear problem
• Mix formulation and h-adaptivity

Step by step tutorial for MoFEM developers. We explain here how to implement general problem on particular examples.

Hierarchical approximation

Introduces the reader to the basic concepts of finite element approach using Hierarchical basis functions.

• Basics of hierarchical approximation

Hello world

Introduces user to basic ideas of user operator and MoFEM::Simple interface and implementation of finite element with users data operators.

• Hello world

The Poisson equation and difussion problems

The Poisson equation is solved using MoFEM::Simple interface. The generic procedure is applied to one of the simples PDEs. In order to make the problem instructional, essential boundary conditions are enforced by Lagrange multipliers.

• Solving the Poisson equation

Tutorial focusses attention on implementation of finite element user operators, setting integration rule and using Tensor template library.

• Implementing operators for the Poisson equation

Example of implementation of nonlinear Poisson equation using SNES (Newton) solver

• A nonlinear Poisson equation

Using PCFIELDSPLIT pre-conditioner to solve problem with Lagrange multipliers

• Using fieldsplit solver and DM sub problem.

Implementation of Fisher's reaction-diffusion equation

• Implementation of reaction-diffusion equation

Solid elasticity problems

Introduction to fundamental MoFEM functionalities and capabilities by solving a simple linear elastic problem.

• Solid elasticity

Tutorial for mixed formulation of incompressible elasticity problem

• Mixed formulation for incompressible elasticity

Tutorial for the implementation of Winkler spring elements

• Implementation of spring element

Nonlinear problem

Minimal surface area (soap film on the wire): Tutorial showing step by step implementation of nonlinear problem. It presents how to set up the problem from scratch, calculate matrices and solve the problem using MoFEM and PETSc

• Soap film spanned on wire

Mix formulation and h-adaptivity

This example shows how to solve transport problem using mix element with an independent approximation for fluxes and function values. Also, it shows how to integrate over mesh skeleton to evaluate error and how to use a posterior error estimator to drive mesh adaptivity (h-adaptivity).

• Mix formulation and integration on skeleton (h-adaptivity)

In this tutorial, we show how to solve time dependent nonlinear problem using mix formulation applied to unsaturated water transport in heterogeneous soil.

• Time dependent nonlinear mix formulation (unsaturated flow)