# Computational Multiscale Methods for Linear Poroelasticity with High Contrast

## TL;DR

This paper presents a multiscale finite element method for efficiently solving high-contrast linear poroelasticity problems, demonstrating convergence and improved computational performance through numerical tests.

## Contribution

It introduces a novel CEM-GMsFEM approach with energy minimization and oversampling for high-contrast poroelasticity, enhancing efficiency and accuracy.

## Key findings

- Method achieves first-order convergence.
- Numerical tests confirm computational efficiency.
- Effective handling of high contrast in coefficients.

## Abstract

In this work, we employ the Constraint Energy Minimizing Generalized Multiscale Finite Element Method (CEM-GMsFEM) to solve the problem of linear heterogeneous poroelasticity with coefficients of high contrast. The proposed method makes use of the idea of energy minimization with suitable constraints in order to generate efficient basis functions for the displacement and the pressure. These basis functions are constructed by solving a class of local auxiliary optimization problems based on eigenfunctions containing local information on the heterogeneity. Techniques of oversampling are adapted to enhance the computational performance. Convergence of first order is shown and illustrated by a number of numerical tests.