Work

A Hybridizable Discontinuous Galerkin Method for the Miscible Displacement Problem under Minimal Regularity

Year: 2026

Type: article

Abstract: . A numerical method based on the hybridizable discontinuous Galerkin method in space and backward Euler in time is formulated and analyzed for solving the miscible displacement problem. Under low regularity assumptions, convergence is established by proving that, up to a subsequence, the discrete pressure, velocity, and concentration converge to a weak solution as the mesh size and time step tend to zero. The analysis is based on several key features: an [Formula: see text] reconstruction of the velocity, the skew-symmetrization of the concentration equation, the introduction of an auxiliary variable, and the definition of a new numerical flux. Numerical examples demonstrate optimal rates of convergence for smooth solutions, and convergence for problems of low regularity.

Source: SIAM Journal on Numerical Analysis

DOI: 10.1137/25m1759239

Authors: Keegan L. A. Kirk, Beatrice Riviere

Institutions: George Mason University, Rice University

Language: English

Topic: Advanced Numerical Methods in Computational Mathematics

Subfield: Computational Mechanics

Field: Engineering

Domain: Physical Sciences

Open Access status: green

Funders: National Science Foundation, Natural Sciences and Engineering Research Council of Canada, Office of Naval Research, Air Force Office of Scientific Research

Awards: G1090354770, G2379414414, G3327059554, Collaborative Research: Multidimensional Couplings for Flow and Transport in Porous Media