Abstract
The goal of this chapter is to demonstrate how a range of important PDEs from science and engineering can be quickly solved with a few lines of FEniCS code. We start with the heat equation and continue with a nonlinear Poisson equation, the equations for linear elasticity, the Navier–Stokes equations, and finally look at how to solve systems of nonlinear advection–diffusion–reaction equations. These problems illustrate how to solve time-dependent problems, nonlinear problems, vector-valued problems, and systems of PDEs. For each problem, we derive the variational formulation and express the problem in Python in a way that closely resembles the mathematics.
Keywords
- Stokes Equation
- Variational Problem
- Heat Equation
- Reaction Equation
- Previous Time Step
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Langtangen, H.P., Logg, A. (2016). A Gallery of Finite Element Solvers. In: Solving PDEs in Python. Simula SpringerBriefs on Computing, vol 3. Springer, Cham. https://doi.org/10.1007/978-3-319-52462-7_3
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DOI: https://doi.org/10.1007/978-3-319-52462-7_3
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Publisher Name: Springer, Cham
Print ISBN: 978-3-319-52461-0
Online ISBN: 978-3-319-52462-7
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