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Grid-based approximation of partial differential equations in Julia

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Gridap provides a set of tools for the grid-based approximation of partial differential equations (PDEs) written in the Julia programming language. The library currently supports linear and nonlinear PDE systems for scalar and vector fields, single and multi-field problems, conforming and nonconforming finite element (FE) discretizations, on structured and unstructured meshes of simplices and n-cubes. Gridap is extensible and modular. One can implement new FE spaces, new reference elements, use external mesh generators, linear solvers, post-processing tools, etc. See, e.g., the list of available Gridap plugins.

Gridap has a very expressive API allowing one to solve complex PDEs with very few lines of code. The user can write the underlying weak form with a syntax almost 1:1 to the mathematical notation, and Gridap generates an efficient FE assembly loop automatically by leveraging the Julia JIT compiler. For instance, the weak form for an interior penalty DG method for the Poisson equation can be simply specified as: ```julia a(u,v) = ∫( ∇(v)⋅∇(u) )dΩ + ∫( (γ/h)vu - v(nΓ⋅∇(u)) - (nΓ⋅∇(v))u )dΓ + ∫( (γ/h)jump(vnΛ)⋅jump(u*nΛ) - jump(vn_Λ)⋅mean(∇(u)) - mean(∇(v))⋅jump(un_Λ) )*dΛ

l(v) = ∫( vf )dΩ + ∫( (γ/h)vu - (n_Γ⋅∇(v))u )

See the complete code [here]( As an example for multi-field PDEs, this is how the weak form for the Stokes equation with Neumann boundary conditions can be specified:
julia a((u,p),(v,q)) = ∫( ∇(v)⊙∇(u) - (∇⋅v)p + q(∇⋅u) )*dΩ

l((v,q)) = ∫( v⋅f + qg )dΩ + ∫( v⋅(nΓ⋅∇u) - (nΓ⋅v)p )dΓ ``` See the complete code here.


  • STABLEDocumentation for the most recently tagged version of Gridap.jl.
  • DEVELDocumentation for the in-development version of Gridap.


A hands-on user-guide to the library is available as a set of tutorials. They are available as Jupyter notebooks and html pages.


Gridap is a registered package in the official Julia package registry. Thus, the installation of Gridap is straight forward using the Julia's package manager. Open the Julia REPL, type

to enter package mode, and install as follows
pkg> add Gridap



These are some popular PDEs solved with the Gridap library. Examples taken from the Gridap Tutorials.

| | | | | |:-------------:|:-------------:|:-----:|:----:| | Poisson equation | Linear elasticity | Hyper-elasticity | p-Laplacian | | | | | | | Poisson eq. with DG | Darcy eq. with RT | Incompressible Navier-Stokes | Isotropic damage |

Known issues

Since Julia 1.6 ownwards we have noticed large first call latencies of Gridap.jl codes with the default compiler optimization level (i.e.,

). In general, while developing code, but specially if you are noting high first call latencies, we recommend to run
with the
flag. For production runs use

## Gridap community

You can ask questions and interact with the Gridap community on the Julia Slack channel #gridap (see here how to join). or our gitter.

Contributing to Gridap

Gridap is a collaborative project open to contributions. If you want to contribute, please take into account:

  • Before opening a PR with a significant contribution, contact the project administrators, e.g., by writing a message in our gitter chat or by opening an issue describing what you are willing to implement. Wait for feed-back.
  • Carefully read and follow the instructions in the file.
  • Carefully read and follow the instructions in the file.
  • Open a PR with your contribution.

Want to help? We have a number of issues waiting for help. You can start contributing to the Gridap project by solving some of those issues.

How to cite Gridap

In order to give credit to the

contributors, we simply ask you to cite the reference below in any publication in which you have made use of the
project. If you are using other
sub-packages, please cite them as indicated in their repositories.
  doi = {10.21105/joss.02520},
  url = {},
  year = {2020},
  publisher = {The Open Journal},
  volume = {5},
  number = {52},
  pages = {2520},
  author = {Santiago Badia and Francesc Verdugo},
  title = {Gridap: An extensible Finite Element toolbox in Julia},
  journal = {Journal of Open Source Software}


Please, contact the project administrators, Santiago Badia and Francesc Verdugo, for further questions about licenses and terms of use.

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