v0.12.1 |

Tutorials

The tutorials contain a number of basic programs that are built on top of each other. Those with the full source code has the following structure

**Introduction**: Problem being solved, mathematical equations and derivations leading to finite element implementation**Implementation**: Detailed explanation of the source code where tasks are separated in different functions**Results**: How to run the program, output, visualisation, interpretation and comments, possible extensions.**Plain program**: Full source code without extended comments

The source code and corresponding binary files of the tutorials are located at the following directories when you install MoFEM with developer version Installation

- Source code:
`$HOME/mofem_install/mofem-cephas/mofem/users_modules/tutorials`

- Binary files (build directory):
`$HOME/mofem_install/mofem-cephas/mofem/users_modules/um-build-RelWithDebInfo-abcd1234/tutorials/`

Each tutorial in this page includes code name and keywords for quick reference and search within the browser.

- Note
- You do not need to go through all the tutorials in the order they are listed in this page before jumping into the topic in which you are interested. However, we do recommend you to have a look at the first few tutorials solving scalar-field problems to have a general idea how the finite element implementation is done in MoFEM. We also make a recommendation at the beginning of each tutorial regarding which tutorial(s) you should read (prerequisites) before continuing with the one you are most excited about.

- Note
- The tutorials are under development. Send us your feedback on Q&A regarding the tutorials that already done and the missing ones that you most prefer to see.

MoFEM Interfaces | Brief introduction about MoFEM interfaces which enable users to implement the codes with different level of complexity. |

FUN-0: Hello world | Creating Simple problem, and pushing operators to pipelines |

FUN-1: Integration on finite element mesh | Numerical integration is essential for most of the numerical methods employed to solve partial differential equations (PDEs) |

FUN-2: Hierarchical approximation | Introduce elementary concepts of the Finite Element Method (FEM) with hierarchical shape functions and their implementation in MoFEM |

MSH-1: Create a 2D mesh from Gmsh | This document shows how to create a MoFEM-compatible 2D input mesh from Gmsh |

MSH-2: Create a 3D mesh from Gmsh | This document shows how to create a MoFEM-compatible 3D input mesh from Gmsh |

SCL-0: Least square approximaton | Solve the least square problem to approximate scalar function |

SCL-1: Poisson's equation (homogeneous BC) | Solve the Poisson's equation with zero value boundary conditions |

SCL-2: Poisson's equation (non-homogeneous BC) | An expansion of previous tutorial to cover non-homogeneous (non-zero value) boundary condition of Poisson's equation |

SCL-3: Poisson's equation (Lagrange multiplier) | Solve the Poisson's equation using Lagrange multiplier for the non-homogeneous boundary condition |

SCL-4: Nonlinear Poisson's equation | Solve nonlinear Poisson's equation using Newton iterative scheme |

SCL-5: Minimal surface equation | A variant of the nonlinear Poisson's equation |

SCL-6: Heat equation | This is the first tutorial to solve a time-dependent problem with first-order time derivative |

SCL-7: Wave equation | Time-dependent problem with second-order time derivative |

SCL-8: Radiation boundary conditions | Nonlinear problem at the boundary |

SCL-9: Heat method | Finding geodesic distance with heat method |

SCL-10: Photon diffusion | Photon diffusion equation |

CLX-0: Helmholtz problem | Helmholtz problem for acoustics |

VEC-0: Linear elasticity | Linear elasticity |

VEC-1: Eigen elastic | Eigen elastic |

VEC-2: Nonlinear elastic | Nonlinear elastic with Hencky material |

VEC-3: Nonlinear dynamic elastic | Time-dependent nonlinear elastic (dynamics) |

VEC-4: Shallow wave equation on sphere | Shallow wave equation on mainfold (atmospheric processes) |

MIX-0: Mixed formulation of Poisson equation | A mixed problem |

DD-0: Transport data driven | Data driven for transport or heat conduction problems |

MAX-0: Magnetostatics | Magnetostatics |

MAX-1: Lorenz force | Lorenz force |

ADV-0: Plastic problem | Plasticity problem |

ADV-1: Contact problem | Contact problem |

ADV-2: Thermo-plastic example | Solve thermo-elasto-plastic probelm |

ADV-3: Various fields and finite element spaces | Problem with various fields and finite element spaces |

ADV-4: Elasticity with spring and rod elements | Problem with mixed dimension (1D, 2D, 3D) |

COR-0: Mixed formulation and integration on skeleton (h-adaptivity) | Mix formulation for transport problem |

COR-1: Time dependent nonlinear mix formulation (unsaturated flow) | Mix formulation for capillary flow |

COR-2: Solving the Poisson equation | Poison equation again with different implementations |

COR-3: Implementing operators for the Poisson equation | Poison equation implementation of differentiation operators |

COR-4: Using fieldsplit solver and DM sub problem. | Poison equation implementation of differentiation operators |

COR-5: A nonlinear Poisson equation | Poison nonlinear equation again |

COR-6: Solid elasticity | Older implementation of elastic problem |

COR-7: Mixed formulation for incompressible elasticity | Older implementation of mixed elastic problem |

COR-8: Implementation of spring element | Implementation of boundary element with springs |

COR-9: Reaction-diffusion equation | Reaction-diffusion Fisher's equation |

COR-10: Navier-Stokes equation | Navier-Stokes equations |

MOD-0: Soap film spanned on wire | Soap film as an external module |

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