IFISS
Using the Incompressible Flow Iterative Solution Software

IFISS: examples which illustrate the use of the Incompressible Flow Iterative Solution Software (IFISS) package, which includes algorithms for discretization by mixed finite element methods and for a posteriori error estimation of the computed solution.

The IFISS package has examples for steady and time dependent versions of

• the Poisson equation;
• the convection-diffusion equation;
• the Stokes equation;
• the Navier-Stokes equation;

Licensing:

The computer code and data files made available on this web page are distributed under the GNU LGPL license.

Related Data and Programs:

DEALII, examples which illustrate the use of DEAL.II, a finite element Differential Equations Analysis Library (DEAL).

DOLFIN, PYTHON scripts which are used with the DOLFIN library to set up and solve a wide variety of problems using the finite element method.

FENICS, programs which illustrate the use of a collection of free software with an extensive list of features for automated, efficient solution of differential equations.

FREEFEM++, a directory of examples which illustrate the use of the FREEFEM++ package, a high-level integrated development environment for the numerical solution of nonlinear multiphysics partial differential equations in 2D and 3D.

IFISS3.3, a MATLAB program which embodies the IFISS software that can model the steady (time-independent) flow of a 2D incompressible fluid, by Howard Elman, Alison Ramage, David Silvester.

TOMS866, a MATLAB library which is version 2.2 of the Incompressible Flow Iterative Solution Software (IFISS), by Howard Elman, Alison Ramage, David Silvester; this is ACM TOMS algorithm 866.

Reference:

1. Howard Elman, Alison Ramage, David Silvester,
   Finite Elements and Fast Iterative Solvers with Applications in Incompressible Fluid Dynamics,
   Oxford, 2005,
   ISBN: 978-0198528678,
   LC: QA911.E39.
2. Howard Elman, Alison Ramage, David Silvester,
   Algorithm 866: IFISS, A Matlab Toolbox for Modelling Incompressible Flow,
   ACM Transactions on Mathematical Software,
   Volume 33, Number 2, June 2007.
3. Howard Elman, Alison Ramage, David Silvester,
   Incompressible Flow Iterative Solution Software (IFISS), Installation and Software Guide,
   http://www.maths.manchester.ac.uk/~djs/ifiss/ifiss_guide_3.0.pdf.
4. William Mitchell,
   A collection of 2D elliptic problems for testing adaptive grid refinement algorithms,
   Applied Mathematics and Computation,
   Volume 220, 1 September 2013, pages 350-364.

Examples and Tests:

ELLIPTIC_WAVEFRONT is a system governed by the steady Poisson equation on the unit square, with Dirichlet boundary conditions, whose solution is a circularly symmetric wave.

• elliptic_wavefront_bc.m, evaluates the boundary conditions.
• elliptic_wavefront_domain.m, defines the geometric information.
• elliptic_wavefront_exact.m, evaluates the exact solution.
• elliptic_wavefront_femq2_diff.m, generates the biquadratic finite element stiffness matrix, mass matrix, and right hand side vector.
• elliptic_wavefront_gauss_source.m, evaluates source terms at Gauss points.
• elliptic_wavefront_nonzerobc.m, imposes Dirichlet boundary conditions.
• elliptic_wavefront_rhs.m, evaluates the right hand side of the PDE.
• elliptic_wavefront_test.m, sets up and solves the problem.
• solution.png, contour and surface plots of the solution.

You can go up one level to the EXAMPLES directory.