7

Yes. The constants that appear in the interpolation estimates upon which finite element error estimates are based contain minimum and maximum angles of triangles/tetrahedra (or similar geometric measures for quadrilaterals/hexahedra). These constants are smallest whenever you have equilateral triangles or square quadrilaterals.


2

It depends on the problem being solved and the element formulation. The orthogonality criterion you state may not be as important as the shape of each element. For example in structural mechanics, with an irregular (e.g. automatically generated and refined) mesh and isoparametric elements, an important criterion for accuracy is the largest angle between ...


1

The equation is derived from momentum balance, so there is nothing wrong with. But you can resolve the apparent paradox like this. Take a square control volume $C = [a,b] \times [c,d]$ and look at x-momentum balance $$ \frac{d}{dt}\int_C \rho u dx dy = -\int_c^d (\rho u^2)(b,y) dy + \int_c^d (\rho u^2)(a,y) dy + \ldots $$ The first term on the right is the ...


1

The eigenvalues given correspond to the flux jacobians in the Euler equations. Physically, they represent the speed at which waves of information can travel in a space-time domain. The goal is to compute the eigenvalues at each face based on the values in each neighboring cell so there is no 'left' or 'right' face in this equation, but instead a left and ...


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