ExactFieldSolutions.jl

Full field solutions are essential for the verification of numerical codes that are based on the solution of Partial Differential Equations (PDE). They allow to check if numerical solutions are meaningful in eyeball norm but, more importantly, they allow to quantify discretisation errors. This quantification further enables to check whether numerical solutions converge to exact solutions at expected theoretical rates. ExactFieldSolutions compiles full field solutions for 2D and 3D PDE problems including Poisson-type and mechanical problems (Stokes, elasticity). Contributions are welcome and full field solutions to other problems (electric, magnetic, MHD) are more than welcome. Feel free to make a PR.

ExactFieldSolutions benefits from automatic differentiation tools available within the Julia ecosystem (e.g., ForwardDiff). These allow to evaluate fluxes and sources terms in a simplified way. See this manufactured solution for the 2D Poisson problem.

Please note that ExactFieldSolutions is a registered package, so you can install it simply by typing add ExactFieldSolutions in package mode.

Poisson 2D

Sevilla et al. (2018)

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Poisson 3D

Sevilla et al. (2018)

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Diffusion 2D

Diffusion of a 2D Gaussian

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Stokes 2D

Viscous inclusion - Schmid & Podladchikov (2003)

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Double corner flow - Moulas et al., (2021)

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Donea & Huerta (2003)

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SolKz - Zhong et al. (1996)

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SolCx - Zhong et al. (1996)

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Elasticity 2D

Elastic plate with a hole

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