Related papers: On Properties of Adjoint Systems for Evolutionary …
For the general class of residual distribution (RD) schemes, including many finite element (such as continuous/discontinuous Galerkin) and flux reconstruction methods, an approach to construct entropy conservative/ dissipative…
Convergence results are shown for full discretizations of quasilinear parabolic partial differential equations on evolving surfaces. As a semidiscretization in space the evolving surface finite element method is considered, using a…
Many important physical systems can be described as the evolution of a Hamiltonian system, which has the important property of being conservative, that is, energy is conserved throughout the evolution. Physics Informed Neural Networks and…
We study the structure-preserving space discretization of port-Hamiltonian (pH) systems defined with differential constitutive relations. Using the concept of Stokes-Lagrange structure to describe these relations, these are reduced to a…
Achieving robust control and optimization in high-fidelity physics simulations is extremely challenging, especially for evolutionary systems whose solutions span vast scales across space, time, and physical variables. In conjunction with…
In this work, we propose a structure-preserving discretisation for the recently studied Cahn-Hilliard-Biot system using conforming finite elements in space and problem-adapted explicit-implicit Euler time integration. We prove that the…
As a counterpoint to recent numerical methods for crystal surface evolution, which agree well with microscopic dynamics but suffer from significant stiffness that prevents simulation on fine spatial grids, we develop a new numerical method…
We propose a finite element discretisation approach for the incompressible Euler equations which mimics their geometric structure and their variational derivation. In particular, we derive a finite element method that arises from a…
In this paper we will consider distributed Linear-Quadratic Optimal Control Problems dealing with Advection-Diffusion PDEs for high values of the P\'eclet number. In this situation, computational instabilities occur, both for steady and…
The aim of this paper is to apply a high-order discontinuous-in-time scheme to second-order hyperbolic partial differential equations (PDEs). We first discretize the PDEs in time while keeping the spatial differential operators…
We want to propose a new discretization ansatz for the second order Hessian complex exploiting benefits of isogeometric analysis, namely the possibility of high-order convergence and smoothness of test functions. Although our approach is…
We discuss the mathematical modeling and numerical discretization of transport problems on one-dimensional networks. Suitable coupling conditions are derived that guarantee conservation of mass across network junctions and dissipation of a…
We consider mechanics of composite materials in which thin inclusions are modeled by lower-dimensional manifolds. By successively applying the dimensional reduction to junctions and intersections within the material, a geometry of…
In this paper we show how almost cosymplectic structures are a natural framework to study thermodynamical systems. Indeed, we are able to obtain the same evolution equations obtained previously by Gay-Balmaz and Yoshimura (see Entropy,…
This work introduces a novel discontinuity-tracking framework for resolving discontinuous solutions of conservation laws with high-order numerical discretizations that support inter-element solution discontinuities, such as discontinuous…
We provide a concise introduction to the symmetry approach to integrability. Some results on integrable evolution and systems of evolution equations are reviewed. Quasi-local recursion and Hamiltonian operators are discussed. We further…
Mixed dimensional partial differential equations (PDEs) are equations coupling unknown fields defined over domains of differing topological dimension. Such equations naturally arise in a wide range of scientific fields including geology,…
We develop a novel iterative algorithm for locally optimal experimental design under constraints, like budget or performance constraints. It is an adaptive discretization algorithm. In every iteration, a discretized version of the…
We develop a high order accurate numerical method for solving the elastic wave equation in second-order form. We hybridize the computationally efficient Cartesian grid formulation of finite differences with geometrically flexible…
In this paper we continue our earlier investigations into the asymptotic behaviour of infinite systems of coupled differential equations. Under the mild assumption that the so-called characteristic function of our system is completely…