Related papers: An energy stable and conservative multiplicative d…
We present a new temporal discretization paradigm for developing energy-production-rate preserving numerical approximations to thermodynamically consistent partial differential equation systems, called the supplementary variable method. The…
In this paper, we propose a robust and efficient numerical framework for simulating multicomponent gas flow in poroelastic media, with a focus on preserving fundamental thermodynamic principles and ensuring computational reliability. The…
This work focuses on the development of a self adjusting multirate strategy based on an implicit time discretization for the numerical solution of hyperbolic equations, that could benefit from different time steps in different areas of the…
This paper addresses the stabilization of dynamical systems in the infinite horizon optimal control setting using nonlinear feedback control based on State-Dependent Riccati Equations (SDREs). While effective, the practical implementation…
We consider the Dynamical Low Rank (DLR) approximation of random parabolic equations and propose a class of fully discrete numerical schemes. Similarly to the continuous DLR approximation, our schemes are shown to satisfy a discrete…
We present a finite-difference integration algorithm for solution of a system of differential equations containing a diffusion equation with nonlinear terms. The approach is based on Crank-Nicolson method with predictor-corrector algorithm…
The numerical approximation of high-dimensional evolution equations poses significant computational challenges, particularly in kinetic theory and radiative transfer. In this work, we introduce the Galerkin Alternating Projection (GAP)…
We propose and analyze a linearly stabilized semi-implicit diffusive Crank--Nicolson scheme for the Cahn--Hilliard gradient flow. In this scheme, the nonlinear bulk force is treated explicitly with two second-order stabilization terms. This…
In this work, we propose a Crank-Nicolson-type scheme with variable steps for the time fractional Allen-Cahn equation. The proposed scheme is shown to be unconditionally stable (in a variational energy sense), and is maximum bound…
In this work, we construct novel discretizations for the unsteady convection-diffusion equation. Our discretization relies on multiderivative time integrators together with a novel discretization that reduces the total number of unknowns…
We present a high-order space-time discretization equipped with fully-discrete entropy stability properties for general choices of volume and surface quadrature rules. The formulation uses flux reconstruction (FR) in the spatial dimension…
We introduce and analyse a fully discrete approximation for a mathematical model for the solidification and liquidation of materials of negligible specific heat. The model is a two-sided Mullins--Sekerka problem. The discretization uses…
We present and analyze a discontinuous Galerkin method for the numerical modelling of the non-linear fully-coupled thermo-poroelastic problem. For the spatial discretization, we design a high-order discontinuous Galerkin method on polygonal…
We proposed a novel dense line spectrum super-resolution algorithm, the DMRA, that leverages dynamical multi-resolution of atoms technique to address the limitation of traditional compressed sensing methods when handling dense point-source…
We consider the discretization and subsequent model reduction of a system of partial differential-algebraic equations describing the propagation of pressure waves in a pipeline network. Important properties like conservation of mass,…
We propose an Eulerian-Lagrangian (EL) Runge-Kutta (RK) discontinuous Galerkin (DG) method for wave equations. The method is designed based on the ELDG method for transport problems [J. Comput. Phy. 446: 110632, 2021.], which tracks…
This work introduces reduced models based on Continuous Low Rank Adaptation (CoLoRA) that pre-train neural networks for a given partial differential equation and then continuously adapt low-rank weights in time to rapidly predict the…
This research article discusses a numerical solution of the radiative transfer equation based on the weak Galerkin finite element method. We discretize the angular variable by means of the discrete-ordinate method. Then the resulting…
In this paper, we develop a high order structure-preserving local discontinuous Galerkin (DG) scheme for the compressible self-gravitating Euler equations, which pose great challenges due to the presence of time-dependent gravitational…
This work investigates the design and analysis of energy-decay preserving numerical schemes for Maxwell's equations in a Cole-Cole (C-C) dispersive medium. A continuous energy-decay law is first established for the C-C model through a…