This module shows by way of examples that how to use dune-PDELab to actually solve PDEs. This tutorial is also used in the Dune Spring School held every year in march in Heidelberg.
The PDELab tutorial consists of examples numbered tutorial00, tutorial01, …. Each tutorial provides exactly one executable and contains the following subdirectories:
srcC++ source code of the example and corresponding executable in the build tree
docdocumentation in LaTeX source form, the pdf is found in the build tree
slidesoptional set of slides if the example is used in the Dune course
exerciseoptional set of exercises for the Dune course
This structure is meant to be extendable in the future. So feel free to add more tutorials that you find useful!
Although each tutorial is self contained it makes sense to work through them in a certain order, depending on what you want to use PDELab for (see the list of tutorials below). A good way to start your own code is then to copy the tutorial which is “closest” to your application. Currently the following tutorials are provided:
tutorial00Piecewise linear finite elements for solving the Poisson equation with Dirichlet boundary conditions on simplicial meshes. Works in dimension 1, 2, 3.
tutorial01Solves Poisson equation with a nonlinear reaction term and Dirichlet as well as Neumann type boundary conditions. Conforming “Lagrange” finite elements with selectable polynomial degree on simplicial and cuboid meshes in dimension 1, 2, 3 can be used.
tutorial02The same equation as in tutorial01 is solved with the cell-centered finite volume method using two-point flux approximation. This method is restricted to axi-parallel, cuboid meshes.
tutorial03Solves instationary diffusion-reaction equation (with nonlinear reaction term) using a method of lines approach. Conforming finite elements of selectable order are used in space and diagonally implicit Runge-Kutta methods are used in time.
tutorial04Solves the wave equation written as a first-order in time system, thereby extending the methods of tutorial03 to systems of partial differential equations.
tutorial05Illustrates how to use adaptive mesh refinement in tutorial01.
tutorial06Illustrates how to extend tutorial01 for parallel computation.