Related papers: Galerkin Approximation of Dynamical Quantities usi…
We consider semi-discrete discontinuous Galerkin approximations of a general elastodynamics problem, in both {\it displacement} and {\it displacement-stress} formulations. We present the stability analysis of all the methods in the natural…
In this note we shall devise a variable-order continuous Galerkin time stepping method which is especially geared towards norm-preserving dynamical systems. In addition, we will provide an a posteriori estimate for the $L^\infty$-error.
Ever since the concepts of dynamic programming were introduced, one of the most difficult challenges has been to adequately address high-dimensional control problems. With growing dimensionality, the utilisation of Deep Neural Networks…
The subject of this work is an adaptive stochastic Galerkin finite element method for parametric or random elliptic partial differential equations, which generates sparse product polynomial expansions with respect to the parametric…
We construct entropy conservative and entropy stable high order accurate discontinuous Galerkin (DG) discretizations for time-dependent nonlinear hyperbolic conservation laws on curvilinear meshes. The resulting schemes preserve a…
We establish global stability for a chemotaxis-growth model with logarithmic sensitivity under dynamic Dirichlet boundary conditions on a 1D domain. We analyze both parabolic-parabolic and parabolic-hyperbolic systems. The key challenge is…
An efficient time-stepping algorithm is proposed based on operator-splitting and the space-time discontinuous Galerkin finite element method for problems in the non-classical theory of thermoelasticity. The non-classical theory incorporates…
We introduce a new method to accurately and efficiently estimate the effective dynamics of collective variables in molecular simulations. Such reduced dynamics play an essential role in the study of a broad class of processes, ranging from…
Observing stochastic trajectories with rare transitions between states, practically undetectable on time scales accessible to experiments, makes it impossible to directly quantify the entropy production and thus infer whether and how far…
Many real-world systems modeled using differential equations involve unknown or uncertain parameters. Standard approaches to address parameter estimation inverse problems in this setting typically focus on estimating constants; yet some…
We present a new numerical approach for wave induced dynamic fracture. The method is based on a discontinuous Galerkin approximation of the first-order hyperbolic system for elastic waves and a phase-field approximation of brittle fracture…
We develop an efficient sampling method by simulating Langevin dynamics with an artificial force rather than a natural force by using the gradient of the potential energy. The standard technique for sampling following the predetermined…
Discontinuous Galerkin (DG) methods have a long history in computational physics and engineering to approximate solutions of partial differential equations due to their high-order accuracy and geometric flexibility. However, DG is not…
Fourier continuation is an approach used to create periodic extensions of non-periodic functions in order to obtain highly-accurate Fourier expansions. These methods have been used in PDE-solvers and have demonstrated high-order convergence…
A general theory is developed to study individual based models which are discrete in time. We begin by constructing a Markov chain model that converges to a one-dimensional map in the infinite population limit. Stochastic fluctuations are…
Computing the distribution of trajectories from a Gaussian Process model of a dynamical system is an important challenge in utilizing such models. Motivated by the computational cost of sampling-based approaches, we consider approximations…
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…
A discontinuous Galerkin method has been developed for strain gradient-dependent damage. The strength of this method lies in the fact that it allows the use of $C^0$ interpolation functions for continuum theories involving higher-order…
The discontinuous Galerkin dG method provides a robust and flexible technique for the time integration of fractional diffusion problems. However, a practical implementation uses coefficients defined by integrals that are not easily…
We propose a new Neural Galerkin Normalizing Flow framework to approximate the transition probability density function of a diffusion process by solving the corresponding Fokker-Planck equation with an atomic initial distribution,…