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We analyse three time integration schemes for unfitted methods in fluid structure interaction. In Alghorithm 1 we propose a fully discrete monolithic algorithm with P1 P1 stabilized finite elements for the fluid problem; for this alghorithm…
We consider the vertex-centered finite volume method with first-order conforming ansatz functions. The adaptive mesh-refinement is driven by the local contributions of the weighted-residual error estimator. We prove that the adaptive…
In this paper, we develop a new multiphysics finite element method for a nonlinear poroelastic model with Hencky-Mises stress tensor. By introducing some new notations, we reformulate the original model into a fluid-fluid coupling problem,…
A cell-centered implicit-explicit updated Lagrangian finite volume scheme on unstructured grids is proposed for a unified first order hyperbolic formulation of continuum fluid and solid mechanics. The scheme provably respects the stiff…
In this paper, a semi-discrete spatial finite volume (FV) method is proposed and analyzed for approximating solutions of anomalous subdiffusion equations involving a temporal fractional derivative of order $\alpha \in (0,1)$ in a…
In molecular dynamics, penalized overdamped Langevin dynamics are used to model the motion of a set of particles that follow constraints up to a parameter $\varepsilon$. The most used schemes for simulating these dynamics are the Euler…
We propose two algorithms for the solution of the optimal control of ergodic McKean-Vlasov dynamics. Both algorithms are based on approximations of the theoretical solutions by neural networks, the latter being characterized by their…
A method is developed to numerically solve chance constrained optimal control problems. The chance constraints are reformulated as nonlinear constraints that retain the probability properties of the original constraint. The reformulation…
By combining concepts from particle-in-cell (PIC) and hybridized discontinuous Galerkin (HDG) methods, we present a particle-mesh scheme which allows for diffusion-free advection, satisfies mass and momentum conservation principles in a…
This article proposes a highly accurate and conservative method for hyperbolic systems using the finite volume approach. This innovative scheme constructs the intermediate states at the interfaces of the control volumes using the method of…
Enlightened from the inverse consideration of the stable continuous-time dynamics evolution, the Variation Evolving Method (VEM) analogizes the optimal solution to the equilibrium point of an infinite-dimensional dynamic system and solves…
The fluid flow transport and hydrodynamic problems often take the form of hyperbolic systems of conservation laws. In this work we will present a new scheme of finite volume methods for solving these evolution equations. It is a family of…
We introduce new hybridizable discontinuous Galerkin (HDG) methods for solving the two-dimensional vector Laplacian equation under three types of boundary conditions: electric, magnetic, and Dirichlet. The method is formulated on a…
This work is devoted to the study of a posteriori error estimation and adaptivity in parabolic problems with a particular focus on spatial discontinuous Galerkin (dG) discretisations. We begin by deriving an a posteriori error estimator for…
We propose a variational approach to identification of an optimal nonlinear eddy viscosity as a subscale turbulence representation for POD models. The ansatz for the eddy viscosity is given in terms of an arbitrary function of the resolved…
The purpose of this work is to propose a novel a posteriori finite volume subcell limiter technique for the Discontinuous Galerkin finite element method for nonlinear systems of hyperbolic conservation laws in multiple space dimensions that…
This article provides quasi-optimal a priori error estimates for an optimal control problem constrained by an elliptic obstacle problem where the finite element discretization is carried out using the symmetric interior penalty…
The aim of this paper is to analyze a mixed discontinuous Galerkin discretization of the time-harmonic elasticity problem. The symmetry of the Cauchy stress tensor is imposed weakly, as in the traditional dual-mixed setting. We show that…
This paper presents a pressure-robust discretizations, specifically within the context of optimal control problems for the Stokes-Darcy system. The study meticulously revisits the formulation of the divergence constraint and the enforcement…
We present and compare third- as well as fifth-order accurate finite difference schemes for the numerical solution of the compressible ideal MHD equations in multiple spatial dimensions. The selected methods lean on four different…