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The two weak formulations of the Stokes equation, $$\int_\Omega\bigl(\nabla\mathbf{v}\cdot\nabla\psi_i+\psi_i\nabla p \bigr) dV=0,$$ and $$\int_\Omega\bigl(\nabla\mathbf{v}\cdot\nabla\psi_i-p \nabla\psi_i\bigr) dV=0,$$ with $\psi_i$ a test function which vanishes on the boundary of $\Omega$, are both in use. (For the first formulation without partial integration of the pressure term, see Burkardt's lecture notes, section 4.)

The first formulation requires that both the velocity field and the pressure field must be $C^1(\Omega)$, in the second formulation the pressure can be $C^0(\Omega)$. There may be reasons why one requirement is favored over the other.

The two weak formulations of the Stokes equation, $$\int_\Omega\bigl(\nabla\mathbf{v}\cdot\nabla\psi_i+\psi_i\nabla p \bigr) dV=0,$$ and $$\int_\Omega\bigl(\nabla\mathbf{v}\cdot\nabla\psi_i-p \nabla\psi_i\bigr) dV=0,$$ with $\psi_i$ a test function which vanishes on the boundary of $\Omega$, are both in use. (For the first formulation without partial integration of the pressure term, see Burkardt's lecture notes, section 4.)

The first formulation requires that both the velocity field and the pressure field must be $C^1(\Omega)$, in the second formulation the pressure can be $C^0(\Omega)$. It depends on application-specific reasons whether one requirement is favored over the other.

The two formulations $$\int_\Omega\bigl(\nabla\mathbf{v}\cdot\nabla\psi_i+\psi_i\nabla p \bigr) dV=0,$$ and $$\int_\Omega\bigl(\nabla\mathbf{v}\cdot\nabla\psi_i-p \nabla\psi_i\bigr) dV=0,$$ with $\psi_i$ a test function which vanishes on the boundary of $\Omega$, are both in use. (For the first formulation without partial integration of the pressure, see Burkardt's lecture notes, section 4.)

The first formulation requires that both the velocity field and the pressure field must be $C^1(\Omega)$, in the second formulation the pressure can be $C^0(\Omega)$. There may be reasons why one requirement is favored over the other.

The two weak formulations of the Stokes equation, $$\int_\Omega\bigl(\nabla\mathbf{v}\cdot\nabla\psi_i+\psi_i\nabla p \bigr) dV=0,$$ and $$\int_\Omega\bigl(\nabla\mathbf{v}\cdot\nabla\psi_i-p \nabla\psi_i\bigr) dV=0,$$ with $\psi_i$ a test function which vanishes on the boundary of $\Omega$, are both in use. (For the first formulation without partial integration of the pressure term, see Burkardt's lecture notes, section 4.)

The first formulation requires that both the velocity field and the pressure field must be $C^1(\Omega)$, in the second formulation the pressure can be $C^0(\Omega)$. There may be reasons why one requirement is favored over the other.

The two formulations $$\int_\Omega\bigl(\nabla\mathbf{v}\cdot\nabla\psi_i+\psi_i\nabla p \bigr) dV=0,$$ and $$\int_\Omega\bigl(\nabla\mathbf{v}\cdot\nabla\psi_i-p \nabla\psi_i\bigr) dV=0,$$ with $\psi_i$ a test function which vanishes on the boundary of $\Omega$, are both in use. (For the first formulation without partial integration of the pressure, see Burkardt's lecture notes, section 4.)

The first formulation requires that both the velocity field and the pressure field must be $C^1(\Omega)$, in the second formulation the pressure can be $C^0(\Omega)$. There may be reasons where one requirement is favored over the other.

The two formulations $$\int_\Omega\bigl(\nabla\mathbf{v}\cdot\nabla\psi_i+\psi_i\nabla p \bigr) dV=0,$$ and $$\int_\Omega\bigl(\nabla\mathbf{v}\cdot\nabla\psi_i-p \nabla\psi_i\bigr) dV=0,$$ with $\psi_i$ a test function which vanishes on the boundary of $\Omega$, are both in use. (For the first formulation without partial integration of the pressure, see Burkardt's lecture notes, section 4.)

The first formulation requires that both the velocity field and the pressure field must be $C^1(\Omega)$, in the second formulation the pressure can be $C^0(\Omega)$. There may be reasons why one requirement is favored over the other.