# For the vector form of the finite element model of momentum and continuity equations MΔ+K^11Δ+K^12P=0, what is the correct expression for mass matrix M?

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For the vector form of the finite element model of momentum and continuity equations MΔ+K^11Δ+K^12P=0, what is the correct expression for mass matrix M?

(a) M=∫Ωcρψ^Tψdx

(b) M=∫Ωcfψ^Tψdx

(c) M=∫Ωctψ^Tψdx

(d) M=∫ΩcPψ^Tψdx

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I need to ask this question from Velocity topic in chapter Flows of Viscous Incompressible Fluids of Finite Element Method

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The correct option is (a) M=∫Ωcρψ^Tψdx

For explanation I would say: The vector form of the finite element model in the flow domain is , MΔ+K^11Δ+K^12P=F^1 where F is force matrix, M is a mass matrix, K^11 is related to velocity term, K^12 is related to the pressure term, P is the pressure matrix, and Δ is the velocity matrix. M is a mass matrix as it contains the mass density values of elements, thus M=∫Ωcρψ^Tψdx, where ρ denotes the mass density.

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