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In this paper we consider the problem of distributed nonlinear optimisation of a separable convex cost function over a graph subject to cone constraints. We show how to generalise, using convex analysis, monotone operator theory and…
Optimization of frame structures is formulated as a~non-convex optimization problem, which is currently solved to local optimality. In this contribution, we investigate four optimization approaches: (i) general non-linear optimization, (ii)…
To obtain the highest confidence on the correction of numerical simulation programs for the resolution of Partial Differential Equations (PDEs), one has to formalize the mathematical notions and results that allow to establish the soundness…
Non-linear convection-reaction-diffusion (CRD) partial differential equations (PDEs) are crucial for modeling complex phenomena in fields such as biology, ecology, population dynamics, physics, and engineering. Numerical approximation of…
Numerically solving high-dimensional random parametric PDEs poses a challenging computational problem. It is well-known that numerical methods can greatly benefit from adaptive refinement algorithms, in particular when functional…
In order to generate initial data for nonlinear relativistic simulations, one needs to solve the Einstein constraints, which can be cast into a coupled set of nonlinear elliptic equations. Here we present an approach for solving these…
We present a general family of subcell limiting strategies to construct robust high-order accurate nodal discontinuous Galerkin (DG) schemes. The main strategy is to construct compatible low order finite volume (FV) type discretizations…
In this paper we present a new H(div)-conforming unfitted finite element method for the mixed Poisson problem which is robust in the cut configuration and preserves conservation properties of body-fitted finite element methods. The key is…
In this paper convexity constraints are derived for a background model of electron energy loss spectra (EELS) that is linear in the fitting parameters. The model outperforms a power-law both on experimental and simulated backgrounds,…
We use partial differential equations (PDEs) to describe physical systems. In general, these equations include evolution and constraint equations. One method used to find solutions to these equations is the Free-evolution approach, which…
In this thesis we develop a stabilised finite element method for solving the equations of poroelasticity to enable solving complex models of biological tissues such as the human lungs. For the proposed numerical scheme, we use the lowest…
This article studies structure-preserving discretizations of Hilbert complexes with nonconforming spaces that rely on projections onto an underlying conforming subcomplex. This approach follows the conforming/nonconforming Galerkin (CONGA)…
We construct a finite element approximation of a strain-limiting elastic model on a bounded open domain in $\mathbb{R}^d$, $d \in \{2,3\}$. The sequence of finite element approximations is shown to exhibit strong convergence to the unique…
This paper is concerned with the development of weak Galerkin (WG) finite element method for optimal control problems governed by second order elliptic partial differential equations (PDEs). It is advantageous to use discontinuous finite…
We develop and evaluate a method for learning solution operators to nonlinear problems governed by partial differential equations (PDEs). The approach is based on a finite element discretization and aims at representing the solution…
We consider the construction of locally conservative fluxes by means of a simple post-processing technique obtained from the finite element solutions of advection diffusion equations. It is known that a naive calculation of fluxes from…
Within recent years, considerable progress has been made regarding high-performance solvers for Partial Differential Equations (PDEs), yielding potential gains in efficiency compared to industry standard tools. However, the latter largely…
Partial Differential Equations (PDEs) describe phenomena ranging from turbulence and epidemics to quantum mechanics and financial markets. Despite recent advances in computational science, solving such PDEs for real-world applications…
We study continuous finite element dicretizations for one dimensional hyperbolic partial differential equations. The main contribution of the paper is to provide a fully discrete spectral analysis, which is used to suggest optimal values of…
Over the past few years, neural network methods have evolved in various directions for approximating partial differential equations (PDEs). A promising new development is the integration of neural networks with classical numerical…