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Questions related to the calculation or use of the Jacobian matrix or its determinant. Not to be confused with the Jacobi iterative method for solving systems of linear equations. For those, use [iterative-method] instead.

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Sanity checking jacobians for Finite Element code

Well, the first obvious test is to check if the determinant of the Jacobian matrix is positive. If it not, it means that your element has inverted and your answer is going to be invalid. … For a unit test you could rotate a triangle 360 degrees by increment of 1 degree and measure that the jacobian is always of determinant 1... …
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