arXiv subjects

Yi-Yung Yang

Publications and source records attributed to Yi-Yung Yang.

3 recordsLinked to original sources

arXiv2026

A Posteriori Error Estimation for Parabolic Equations with Enriched Galerkin Finite Element Methods

This paper introduces a novel a posteriori error estimation framework for the enriched Galerkin (EG) finite element method applied to linear parabolic equations. While the EG method has been recognized for its local conservation property and computational efficiency compared to discontinuous Galerkin methods, its mathematical analysis in the context of a posteriori error estimation for parabolic problems remains unexplored. In this work, we prove reliability and efficiency using the residual-based approach. Furthermore, we integrate these error estimators into an adaptive mesh refinement strategy, demonstrating their effectiveness in achieving efficient and reliable error control through several numerical examples. The proposed approach provides a significant advancement in the mathematical foundation and practical applicability of the EG method for time-dependent problems.

math.NA↗

arXiv2026

Heat Transfer Modeling in Enhanced Geothermal Energy: A Three-Temperature Approach for Solid, Injected, and Residing Fluids

Enhanced geothermal systems (EGS) involve strongly coupled, advection-dominated flow and heat transfer in fractured porous media. Conventional models typically assume local thermal equilibrium with a single effective fluid temperature or, at best, an averaged pore-fluid temperature, so the thermal evolution of injected cold fluid is only inferred indirectly. In this work, we develop a local thermal non-equilibrium (LTNE) model that explicitly resolves the temperature of injected fluid as it moves through the reservoir and exchanges heat with the hot rock and resident fluid. The key ingredient is a concentration variable that tracks the injected fluid and induces a three-way LTNE coupling among rock, resident-fluid, and injected-fluid temperatures. This framework distinguishes, at the continuum scale, how newly injected fluid parcels are heated by conductive and convective exchange, and predicts production-well temperatures without relying on bulk averages. To discretize the resulting nonlinear, advection-dominated system, we employ an enriched Galerkin (EG) finite element method for Darcy flow, temperature, and concentration, providing local mass conservation with relatively few degrees of freedom. We further design a flux-corrected transport (FCT) strategy for the EG concentration and temperature equations to enforce a discrete maximum principle and suppress nonphysical oscillations while preserving local conservation. Time integration uses an IMPES-type splitting combined with a strong-stability-preserving Runge--Kutta scheme. Numerical experiments for fractured EGS problems show that the proposed LTNE--EG--FCT framework captures injected-fluid heating paths and thermal breakthrough behavior not resolved by standard single-temperature or averaged LTNE models.

math.NA↗

arXiv2024

Bound-preserving and entropy stable enriched Galerkin methods for nonlinear hyperbolic equations

In this paper, we develop monolithic limiting techniques for enforcing nonlinear stability constraints in enriched Galerkin (EG) discretizations of nonlinear scalar hyperbolic equations. To achieve local mass conservation and gain control over the cell averages, the space of continuous (multi-)linear finite element approximations is enriched with piecewise-constant functions. The resulting spatial semi-discretization has the structure of a variational multiscale method. For linear advection equations, it is inherently stable but generally not bound preserving. To satisfy discrete maximum principles and ensure entropy stability in the nonlinear case, we use limiters adapted to the structure of our locally conservative EG method. The cell averages are constrained using a flux limiter, while the nodal values of the continuous component are constrained using a clip-and-scale limiting strategy for antidiffusive element contributions. The design and analysis of our new algorithms build on recent advances in the fields of convex limiting and algebraic entropy fixes for finite element methods. In addition to proving the claimed properties of the proposed approach, we conduct numerical studies for two-dimensional nonlinear hyperbolic problems. The numerical results demonstrate the ability of our limiters to prevent violations of the imposed constraints, while preserving the optimal order of accuracy in experiments with smooth solutions.

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