Divergence Preserving Interpolation on Anisotropic Quadrilateral Meshes

Abstract For the solution of incompressible fluid models with inf-sup stable finite element pairs for velocity and pressure, interpolation operators are desirable which preserve the property of discrete zero divergence and enjoy the same local approximation properties as standard interpolation operators. In this work, we show how an anisotropic interpolation operator can be modified preserving the discrete divergence and maintaining certain anisotropic interpolation properties. Beside the construction of such an operator for special anisotropic meshes, we discuss the applicability of anisotropic grid resolution of boundary layers for incompressible low-turbulent flow problems.

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