Related papers: Parallelisation of partial differential equations …
This article discusses nonconforming finite element methods for convex minimization problems and systematically derives dual mixed formulations. Duality relations lead to simple error estimates that avoid an explicit treatment of…
This article focuses on those aspects about partial actions of groups which are related to Schur's theory on projective representations. It provides an exhaustive description of the partial Schur multiplier, and this result is achieved by…
Coarse grained, macroscale, spatial discretisations of nonlinear nonautonomous partial differential\difference equations are given novel support by centre manifold theory. Dividing the physical domain into overlapping macroscale elements…
The effective, fast transport of matter through porous media is often characterized by complex dispersion effects. To describe in mathematical terms such situations, instead of a simple macroscopic equation (as in the classical Darcy's…
A large toolbox of numerical schemes for dispersive equations has been established, based on different discretization techniques such as discretizing the variation-of-constants formula (e.g., exponential integrators) or splitting the full…
We consider a linear inverse problem whose solution is expressed as a sum of two components: one smooth and the other sparse. This problem is addressed by minimizing an objective function with a least squares data-fidelity term and a…
A probabilistic representation for initial value semilinear parabolic problems based on generalized random trees has been derived. Two different strategies have been proposed, both requiring generating suitable random trees combined with a…
We explore how the analysis of the Carleman linearization can be extended to dynamical systems on infinite-dimensional Hilbert spaces with quadratic nonlinearities. We demonstrate the well-posedness and convergence of the truncated Carleman…
For uncertainty propagation of highly complex and/or nonlinear problems, one must resort to sample-based non-intrusive approaches [1]. In such cases, minimizing the number of function evaluations required to evaluate the response surface is…
Spectral discretizations of fractional derivative operators are examined, where the approximation basis is related to the set of Jacobi polynomials. The pseudo-spectral method is implemented by assuming that the grid, used to represent the…
Constructing discrete models of stochastic partial differential equations is very delicate. Stochastic centre manifold theory provides novel support for coarse grained, macroscale, spatial discretisations of nonlinear stochastic partial…
In this work we study the dynamic behaviour of compound shells of revolution partially filled with an ideal incompressible fluid based on boundary-value problems. New analytical mathematical model with corresponding discrete scheme for the…
In this work, we consider alternative discretizations for PDEs which use expansions involving integral operators to approximate spatial derivatives. These constructions use explicit information within the integral terms, but treat boundary…
Partial differential equations (PDEs) describing thermodynamically isolated systems typically possess conserved quantities (like mass, momentum, and energy) and dissipated quantities (like entropy). Preserving these conservation and…
For discretisations of hyperbolic conservation laws, mimicking properties of operators or solutions at the continuous (differential equation) level discretely has resulted in several successful methods. While well-posedness for nonlinear…
The geometrical theory of partial differential equations in the absolute sense, without any additional structures, is developed. In particular the symmetries need not preserve the hierarchy of independent and dependent variables. The order…
Coupled multi-physics problems are encountered in countless applications and pose significant numerical challenges. Although monolithic approaches offer possibly the best solution strategy, they often require ad-hoc preconditioners and…
We show that the exact discrete analogue of Schr\"odinger equation can be derived naturally from the Hamiltonian operator of a Schr\"odinger field theory by using the discrete Fourier transform that transforms the operator from momentum…
We analyze the method for calculation of properties of non-relativistic quantum systems based on exact diagonalization of space-discretized short-time evolution operators. In this paper we present a detailed analysis of the errors…
Forman introduced discrete Morse theory as a tool for studying CW complexes by essentially collapsing them onto smaller, simpler-to-understand complexes of critical cells in [Fo]. Chari reformulated discrete Morse theory for regular cell…