Conservation properties of non-conforming embedded finite-element methods based on lagrange multipliers

Area of Science:

• Computational fluid dynamics
• Porous media physics
• Numerical analysis

Background:

• Darcy flow simulations in fractured porous media often use hybrid or equi-dimensional fracture models.
• Mesh generation for fractured media presents significant challenges.
• Local conservation properties of embedded strategies in Continuous Galerkin (CG) discretizations remain under-investigated.

Purpose of the Study:

• To demonstrate the local conservation properties of embedded strategies for fractured porous media.
• To analyze the conservation characteristics of both hybrid and equi-dimensional fracture models.
• To validate the use of embedded strategies within a Continuous Galerkin framework.

Main Methods:

• Utilized embedded strategies employing dual Lagrange multipliers.
• Discretized the models within a Continuous Galerkin framework.
• Conducted numerical analysis focusing on conservation properties.

Main Results:

• Embedded strategies, when using dual Lagrange multipliers and CG discretization, are locally conservative.
• Numerical analysis confirmed the conservation properties for both hybrid and equi-dimensional models.
• The findings support the reliability of embedded strategies for fractured porous media simulations.

Conclusions:

• Embedded strategies are confirmed to be locally conservative for Darcy flow in fractured porous media.
• This study validates the use of embedded strategies within a Continuous Galerkin framework.
• The results provide strong support for the application of embedded strategies in complex fractured media simulations.