Related papers: Finite Element Approximation of Data-Driven Proble…
We consider the primal and dual forms of the optimality conditions for PDE-contrained optimization problems arising in Data-Driven Computational Mechanics when specialized to the reaction-diffusion context. Starting with the continuous…
We present a novel framework for PDE-constrained $r$-adaptivity of high-order meshes. The proposed method formulates mesh movement as an optimization problem, with an objective function defined as a convex combination of a mesh quality…
We propose a novel finite element method scheme for singularly perturbed advection-diffusion-reaction problems, which combines certain quantum-assisted stabilization scheme with a classical h-adaptive approach to provide automatic error…
We consider a numerical approximation of a linear quadratic control problem constrained by the stochastic heat equation with non-homogeneous Neumann boundary conditions. This involves a combination of distributed and boundary control, as…
In this paper, gradient-based optimization methods are combined with finite-element modeling for improving electric devices. Geometric design parameters are considered by affine decomposition of the geometry or by the design element…
In this paper, we will consider an $hp$-finite elements discretization of a highly indefinite Helmholtz problem by some dG formulation which is based on the ultra-weak variational formulation by Cessenat and Depr\'{e}s. We will introduce an…
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 addresses the research question if and how the finite cell method, an embedded domain finite element method of high order, may be used in the simulation of metal deposition to harvest its computational efficiency. This…
We describe and analyze a hybrid finite element/neural network method for predicting solutions of partial differential equations. The methodology is designed for obtaining fine scale fluctuations from neural networks in a local manner. The…
We consider goal-oriented adaptive space-time finite-element discretizations of the regularized parabolic p-Laplace problem on completely unstructured simplicial space-time meshes. The adaptivity is driven by the dual-weighted residual…
We propose a new class of finite element approximations to ideal compressible magnetohydrodynamic equations in smooth regime. Following variational approximations developed for fluid models in the last decade, our discretizations are built…
We present a novel and comparative analysis of finite element discretizations for a nonlinear Rosenau-Burgers model including a biharmonic term. We analyze both continuous and mixed finite element approaches, providing stability, existence,…
Numerical approximations of partial differential equations (PDEs) are routinely employed to formulate the solution of physics, engineering, and mathematical problems involving functions of several variables, such as the propagation of heat…
We present a computationally efficient approach to solve the time-dependent Kohn-Sham equations in real-time using higher-order finite-element spatial discretization, applicable to both pseudopotential and all-electron calculations. To this…
We consider flux-corrected finite element discretizations of 3D convection-dominated transport problems and assess the computational efficiency of algorithms based on such approximations. The methods under investigation include…
We present a fully iterative adaptive algorithm for the numerical minimization of strongly convex energy functionals in Hilbert spaces. The proposed approach, which we first present in abstract form, generates a hierarchical sequence of…
We introduce a data-driven approach to the modelling and analysis of viscous fluid mechanics. Instead of including constitutive laws for the fluid's viscosity in the mathematical model, we suggest to directly use experimental data. Only a…
This paper concerns the inclusion of Newton's method into an adaptive finite element method (FEM) for the solution of nonlinear partial differential equations (PDEs). It features an adaptive choice of the damping parameter in the Newton…
We consider a new class of problems in elasticity, referred to as Data-Driven problems, defined on the space of strain-stress field pairs, or phase space. The problem consists of minimizing the distance between a given material data set and…
We present a domain decomposition formulation based on hybridization which is inspired by hybridized discontinuous Galerkin (HDG) methods, that enhance mixed domain decomposition methods by incorporating stabilization terms. Unlike…