Related papers: Preconditioned space-time boundary element methods…
In this study, we derived a three-dimensional scaled boundary finite element formulation for heat conduction problems. By incorporating Wachspress shape functions, a polyhedral scaled boundary finite element method (PSBFEM) was proposed to…
Implicit solvers for atmospheric models are often accelerated via the solution of a preconditioned system. For block preconditioners this typically involves the factorisation of the (approximate) Jacobian resulting from linearization of the…
The solution to the initial and Dirichlet boundary value problem for a semilinear, one dimensional heat equation is approximated by a numerical method that combines the Besse relaxation scheme in time (C. R. Acad. Sci. Paris S{\'e}r. I,…
We develop a complementarity-constrained nonlinear optimization model for the time-dependent control of district heating networks. The main physical aspects of water and heat flow in these networks are governed by nonlinear and hyperbolic…
In this work, we design and analyze a novel, provably conditionally stable, weakly coupled partitioned scheme to solve the conjugate heat transfer (CHT) problem. We consider a model CHT problem consisting of linear advection-diffusion and…
This work deals with the efficient numerical solution of the time-fractional heat equation discretized on non-uniform temporal meshes. Non-uniform grids are essential to capture the singularities of "typical" solutions of time-fractional…
The first order by time partial differential equations are used as models in applications such as fluid flow, heat transfer, solid deformation, electromagnetic waves, and others. In this paper we propose the new numerical method to solve a…
To predict the heat diffusion in a given region over time, it is often necessary to find the numerical solution for heat equation. With the techniques of discrete differential calculus, we propose two unconditional stable numerical schemes…
We consider two steady-state heat conduction systems called, $S$ and $S_\alpha$, in a multidimensional bounded domain $D$ for the Poisson equation with source energy $g$. In one system, we impose mixed boundary conditions (temperature $b$…
A fully discrete approximation of the one-dimensional stochastic heat equation driven by multiplicative space-time white noise is presented. The standard finite difference approximation is used in space and a stochastic exponential method…
For most finite element simulations, boundary-conforming meshes have significant advantages in terms of accuracy or efficiency. This is particularly true for complex domains. However, with increased complexity of the domain, generating a…
A novel boundary element method (BEM) removes the classical dependence on explicit fundamental solutions and extends quasi-optimal BEM discretisations to strongly elliptic operators with variable coefficients. The approach constructs a…
This paper studies the existence of solutions and, in particular, the well-posedness of a class of boundary control systems. Our main result provides explicit and verifiable conditions on the system data that guarantee continuous dependence…
This article investigates a space-time differential model related to the degradation of stone artifacts caused by exposure to air and atmospheric agents, which specifically lead to the accumulation of salt crystals in the material. A…
This paper formulates variational integrators for finite element discretizations of deformable bodies with heat conduction in the form of finite speed thermal waves. The cornerstone of the construction consists in taking advantage of the…
The paper introduces a new finite element numerical method for the solution of partial differential equations on evolving domains. The approach uses a completely Eulerian description of the domain motion. The physical domain is embedded in…
We evaluate the influence of local resolution, eddy viscosity, coastline structure, and boundary conditions on the numerical representation of boundary currents in a finite element shallow-water model. The use of finite element…
We construct and analyze a preconditioner of the linear elastiity system discretized by conforming linear finite elements in the framework of the auxiliary space method. The auxiliary space preconditioner is based on discretization of a…
We present a novel framework based on semi-bounded spatial operators for analyzing and discretizing initial boundary value problems on moving and deforming domains. This development extends an existing framework for well-posed problems and…
This work proposes a novel variational approximation of partial differential equations on moving geometries determined by explicit boundary representations. The benefits of the proposed formulation are the ability to handle large…