A user-guide to Gridap -- grid-based approximation of partial differential equations in Julia

TL;DR

Gridap is an open-source Julia library that simplifies the development of complex PDE solvers using grid-based approximations, combining ease of use with high performance for various PDE systems.

Contribution

This paper introduces Gridap, a Julia-based framework for PDE approximation that balances user-friendly design with efficient computation, covering diverse discretizations and mesh types.

Findings

Supports scalar and vector PDE systems

Handles conforming and nonconforming finite element discretizations

Operates on structured and unstructured meshes

Abstract

We present Gridap, a new scientific software library for the numerical approximation of partial differential equations (PDEs) using grid-based approximations. Gridap is an open-source software project exclusively written in the Julia programming language. The main motivation behind the development of this library is to provide an easy-to-use framework for the development of complex PDE solvers in a dynamically typed style without sacrificing the performance of statically typed languages. This work is a tutorial-driven user guide to the library. It covers some popular linear and nonlinear PDE systems for scalar and vector fields, single and multi-field problems, conforming and nonconforming finite element discretizations, on structured and unstructured meshes of simplices and hexahedra.