## Software

• ### Short finite element implementation (50 lines of MATLAB)

 Description A short Matlab implementation for P1-Q1 finite elements on triangles and parallelograms is provided for the numerical solution of elliptic problems with mixed boundary conditions on unstructured grids. According to the shortness of the programm and the given documentation, any adaption from simple model examples to more complex problems con easily be performed. Numerical examples prove the flexibility of the Matlab tool. Remarks around 50 lines of Matlab: short finite element implementation -- pdf Software archive
• ### Linear elasticity

Description A short Matlab implementation for P1 and Q1 finite elements is provided for the numerical solution of 2d and 3d problems in linear elasticity with mixed boundary conditions. Any adaption from the simple model examples provided to more complex problems can easily be performed with the given documentation. Numerical examples with postprocessing and error estimation via an averaged stress field illustrate the new Matlab tool and its flexibility. Matlab implementation of the finite element method in elasticity -- pdf Software archive
• ### Elastoviscoplasticity

 Description This example provides a short Matlab implementation with documentation of the P1 finite element method for the numerical solution of viscoplastic and elastoplastic evolution problems in 2D and 3D for von Mises yield functions and Prandtl-Reuß flow rules. The material behaviour includes perfect plasticity as well as isotropic and kinematic hardening with or without a viscoplastic penalisation in a dual model, i.e. with displacements and the stresses as the main variables. The numerical realisation, however, eliminates the internal variables and becomes displacement-oriented in the end. Any adaption from the given three time-depending examples to mor complex applications can easily be performed because of the shortness of the program and the given documentation. In the numerical 2D and 3D examples an efficient error estimator is realized to monitor the stress error. Elastoviscoplastic finite element analysis in 100 lines of Matlab -- pdf Software archive
• ### Mixed finite elements

 Description The numerical approximation of the Laplace equation with inhomogeneous mixed boundary conditions in 2D with lowest-order Raviart-Thomas mixed finite elements is realized in three flexible and short MATLAB programs. The first, hybrid, implementation (LMmfem) is based on Lagrange multiplier techniques. The second, direct, approach (EBmfem) utilizes edge-basis functions for the lowest order Raviart-Thomas finite elements. The third ansatz (CRmfem) utilizes the P1 nonconforming finite element method due to Crouzeix and Raviart and then postprocesses the discrete flux via a technique due to Marini. It is the aim of this paper to derive, document, illustrate, and validate the three MATLAB implementations EBmfem, LMmfem, and CRmfem for further use and modification in education and research. A posteriori error control with a reliable and efficient averaging technique is included to monitor the discretization error. Therein, emphasis is on the correct treatment of mexed boundary conditions. Numerical examples illustrate some applications of the provided software and the quality of the error estimation. Three Matlab implementations of the lowest-order Raviart-Thomas mfem with a posteriori error control -- pdf Software archive
• ### Isoparametric finite elements

Software Software archive