Assume some basic knowledge of numerical methods for PDEs, acquired through A. Quarteroni's Numerical models for differential problems.

I'm looking for a reference to get started on the analysis of PDEs and modeling for industrial problems and related computational approaches (with sample Matlab code available to illustrate them).

Are there monographs that deal with concrete complicated (possibly messy) industrial problems (elasticity, fluid mechanics, continuum mechanics, chemical reactions, etc.) involving PDEs (i.e. PDE models that arise in real-life "industrial" settings)?

I'm looking for rigorous analysis and numerical analysis. Also, I'd prefer if such books included fairly complete source codes of implementations of the proposed numerical algorithms in MATLAB.

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    $\begingroup$ Many of the codes used to solve "industrial" solid mechanics problems (as an example) consist of millions of lines of proprietary code and have been under active development for more than 40 years. There are dozens of books describing the algorithms used. You need to be more specific about what you are looking for. $\endgroup$ – Bill Greene Jan 15 '18 at 22:12
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    $\begingroup$ Not a direct answer to your question, but Skiena's Algorithm Design Manual has several "war stories" about how the author or his colleagues used the principles he illustrates in the book on real-life problems. Many of them are very funny or self-deprecating. It would be great if there were a similar compendium for computational physics. There are lots of resources on solving comparatively simple problems but the chasm between these and real life is awfully wide. $\endgroup$ – Daniel Shapero Jan 15 '18 at 22:25
  • $\begingroup$ Have you read the manual published by NAFEMS? $\endgroup$ – nicoguaro Jan 15 '18 at 23:18
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    $\begingroup$ Many professional organizations with a significant connection to industrial research publish proceedings of papers that are in many cases from industry. For example, the Society of Petroleum Engineers has such proceedings, and there are similar series in aerodynamics, for example. $\endgroup$ – Wolfgang Bangerth Jan 16 '18 at 4:35
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    $\begingroup$ Check out the Society for Industrial and Applied Mathematics (siam.org) and in particular their booklist $\endgroup$ – Philip Roe Jan 18 '18 at 18:42

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