Related papers: A Space-Time DPG Method for the Heat Equation

The aim of this work is to introduce a thermo-electromagnetic model for calculating the temperature and the power dissipated in cylindrical pieces whose geometry var\'ies with time and undergoes large deformations; the motion will be a…

In the presented paper we tackle the problem of the effective field theory in curved spacetime (cEFT) construction. To this end, we propose to use the heat kernel method. After introducing the general formalism based on the well established…

This study investigates the thermal properties of the repulsive Fermi-Hubbard model with chemical potential using variational quantum algorithms, crucial in comprehending particle behaviour within lattices at high temperatures in condensed…

In [2019, Space-time least-squares finite elements for parabolic equations, arXiv:1911.01942] by F\"uhrer& Karkulik, well-posedness of a space-time First-Order System Least-Squares formulation of the heat equation was proven. In the present…

In this paper, we investigate an energy cost minimization problem for a smart home in the absence of a building thermal dynamics model with the consideration of a comfortable temperature range. Due to the existence of model uncertainty,…

We present a family of integral equation-based solvers for the linear or semilinear heat equation in complicated moving (or stationary) geometries. This approach has significant advantages over more standard finite element or finite…

The use of explicit particle-in-cell (PIC) method for relativistic plasma simulations is restricted by numerical heating and instabilities that may significantly constrain the choice of time and space steps. To partially eliminate these…

We present a new explicit and stable numerical algorithm to solve the homogeneous heat equation. We illustrate the performance of the new method in the cases of two 2D systems with highly inhomogeneous random parameters. Spatial…

We consider goal-oriented adaptive space-time finite-element discretizations of the parabolic heat equation on completely unstructured simplicial space-time meshes. In some applications, we are interested in an accurate computation of some…

We study a time fractional heat equation in a noncylindrical domain. The problem is one-dimensional. We prove existence of properly defined weak solutions by means of the Galerkin approximation.

There has been an arising trend of adopting deep learning methods to study partial differential equations (PDEs). This article is to propose a Deep Learning Galerkin Method (DGM) for the closed-loop geothermal system, which is a new coupled…

We present a hybrid quantum-classical framework for solving general time-dependent parabolic partial differential equations (PDEs) using quantum variational circuits. Building on the QPINN approach, this method applies broadly to parabolic…

We consider the discontinuous Petrov-Galerkin (DPG) method, wher the test space is normed by a modified graph norm. The modificatio scales one of the terms in the graph norm by an arbitrary positive scaling parameter. Studying the…

This article introduces the DPG-star (from now on, denoted DPG$^*$) finite element method. It is a method that is in some sense dual to the discontinuous Petrov-Galerkin (DPG) method. The DPG methodology can be viewed as a means to solve an…

We propose a new simple way to evaluate the effect of anharmonicity on a system's thermodynamic functions such as heat capacity. In this approach, the contribution of all potentially complicated anharmonic effects to constant-volume heat…

We develop a space-time spectral element method for topology optimization of transient heat conduction. The forward problem is discretized with summation-by-parts (SBP) operators, and interface/boundary and initial/terminal conditions are…

We consider the finite element (FE) approximation of the shallow water equations (SWE) by considering discretizations in which both space and time are established using an unconditionally stable FE method. Particularly, we consider the…

We propose a Hilbert space solution theory for a nonhomogeneous heat equation with delay in the highest order derivatives with nonhomogeneous Dirichlet boundary conditions in a bounded domain. Under rather weak regularity assumptions on the…

We considered the thermodynamics in spaces with deformed commutation relation leading to existence of the minimal length. We developed a classical method of the partition function evaluation. We calculated the partition function and heat…

In this paper we investigate the asymptotic behavior and decay of the solution of the discrete in time $N$-dimensional heat equation. We give a convergence rate with which the solution tends to the discrete fundamental solution, and the…