# A conservative hybrid method for Darcy flow

## TL;DR

This paper introduces a hybrid mimetic spectral element method for Darcy flow that ensures mass conservation and inter-element continuity, resulting in sparse, mesh-invariant systems that are computationally efficient.

## Contribution

It presents a novel hybrid spectral element formulation that maintains key physical and topological properties for Darcy flow, independent of mesh shape or size.

## Key findings

- Produces extremely sparse algebraic systems
- Efficiently assembled and solved per element
- Invariant under mesh transformations

## Abstract

We present a hybrid mimetic spectral element formulation for Darcy flow. The discrete representations for 1) conservation of mass, and 2) inter-element continuity, are topological relations that lead to sparse matrix systems. These constraints are independent of the element size and shape, and thus invariant under mesh transformations. The resultant algebraic system is extremely sparse even for high degree polynomial basis. Furthermore, the system can be efficiently assembled and solved for each element separately.