We construct and analyze a discontinuous Galerkin method to solve advectiondiffusion-reaction PDEs with anisotropic and semidefinite diffusion. The method is designed to automatically detect the so-called elliptic/hyperbolic interface on fitted meshes. The key idea is to use consistent weighted average and jump operators. Optimal estimates in the broken graph norm are proven. These are consiste...

Four primal discontinuous Galerkin methods are applied to solve reactive transport problems, namely, Oden-Babuška-Baumann DG (OBB-DG), non-symmetric interior penalty Galerkin (NIPG), symmetric interior penalty Galerkin (SIPG), and incomplete interior penalty Galerkin (IIPG). A unified a posteriori residual-type error estimation is derived explicitly for these methods. From the computed solution...

In this work, a flexible higher-order space–time adaptive finite element approximation of convection-dominated transport with coupled fluid flow is developed and studied. Convection-dominated challenging subproblem in poromechanics which flow, chemical reaction mechanical response porous media considered. Key ingredients are the arbitrary degree discontinuous Galerkin time discretization primal...

We devise a stabilized method to weakly enforce bound constraints in the discrete solution of advection-dominated diffusion problems. This combines nonlinear penalty formulation with discontinuous Galerkin-based residual minimization method. illustrate efficiency this scheme for both uniform and adaptive meshes through proper numerical examples.

A reduced basis method based on a physics-informed machine learning framework is developed for efficient reduced-order modeling of parametrized partial differential equations (PDEs). feedforward neural network used to approximate the mapping from time-parameter coefficients. During offline stage, trained by minimizing weighted sum residual loss equations, and data labeled coefficients that are ...

We present a high-order implicit large-eddy simulation (ILES) approach for simulating transitional turbulent flows. The approach consists of an Interior Embedded Discontinuous Galerkin (IEDG) method for the discretization of the compressible Navier-Stokes equations and a parallel preconditioned Newton-GMRES solver for the resulting nonlinear system of equations. The IEDG method arises from the ...

Abstract We study the dynamics of a parabolic and hyperbolic equation coupled on common interface. develop time-stepping schemes that can use different time-step sizes for each subproblems. The problem is formulated in strongly (monolithic) space-time framework. Coupling two step monolithically gives rise to large algebraic systems equations. There, multiple states subproblems must be solved at...