Mantle convection and melt migration are important processes for understanding Earth’s dynamics and how they relate to observations at the surface. Recently it has been established that melt migration can be modelled by coupling variable-viscosity Stokes flow and Darcy flow, where Stokes flow generally captures the long-term behaviour of the mantle and lithosphere, and Darcy flow models the two-phase regime. It is known that approximating the solution by finite element methods requires the use of mixed inf-sup stable elements or additional stabilization terms. Here, we propose a formulation with a coercive non-symmetric linear operator which allows the use of simple equal-order elements.

地幔对流和熔体迁移是了解地球动力学及其与地表观测的关系的重要过程。最近，已经确定可以通过耦合变粘度斯托克斯流和达西流来模拟熔体迁移，其中斯托克斯流通常捕获地幔和岩石圈的长期行为，而达西流则模拟两相状态。众所周知，通过有限元方法近似求解需要使用混合的insup稳定元素或其他稳定项。在这里，我们提出了一种具有强制非对称线性算子的公式，该公式允许使用简单的等阶元素。