Related papers: Higher order temporal finite element methods throu…
We solve elliptic systems of equations posed on highly heterogeneous materials. Examples of this class of problems are composite structures and geological processes. We focus on a model problem which is a second-order elliptic equation with…
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…
Optimization is an important module of modern machine learning applications. Tremendous efforts have been made to accelerate optimization algorithms. A common formulation is achieving a lower loss at a given time. This enables a…
Finite element exterior calculus (FEEC) has been developed as a systematical framework for constructing and analyzing stable and accurate numerical method for partial differential equations by employing differential complexes. This paper is…
In this paper, we study decoupled mixed element schemes for fourth order problems. A general process is designed such that an elliptic problem on high-regularity space is transformed to a decoupled system with spaces of low order involved…
In this paper, new unfitted mixed finite elements are presented for elliptic interface problems with jump coefficients. Our model is based on a fictitious domain formulation with distributed Lagrange multiplier. The relevance of our…
How heterogeneous multiscale methods (HMM) handle fluctuations acting on the slow variables in fast-slow systems is investigated. In particular, it is shown via analysis of central limit theorems (CLT) and large deviation principles (LDP)…
In this contribution we derive and analyze a new numerical method for kinetic equations based on a variable transformation of the moment approximation. Classical minimum-entropy moment closures are a class of reduced models for kinetic…
We propose a high order numerical homogenization method for dissipative ordinary differential equations (ODEs) containing two time scales. Essentially, only first order homogenized model globally in time can be derived. To achieve a high…
Dynamical decoupling techniques constitute an integral part of many quantum sensing platforms, often leading to orders-of-magnitude improvements in coherence time and sensitivity. Most AC sensing sequences involve a periodic echo-like…
In this paper, we introduce new stable mixed finite elements of any order on polytopal mesh for solving second order elliptic problem. We establish optimal order error estimates for velocity and super convergence for pressure. Numerical…
In the analysis of composite materials with heterogeneous microstructures, full resolution of the heterogeneities using classical numerical approaches can be computationally prohibitive. This paper presents a micromechanics-enhanced finite…
The problem of controlling hybrid dynamical systems using model predictive control (MPC) is formulated and sufficient conditions for asymptotic stability of a set are provided. Hybrid dynamical systems are modeled in terms of hybrid…
We establish rigorous \emph{a posteriori} error bounds for a space-time finite element method of arbitrary order discretising linear wave problems in second order formulation. The method combines standard finite elements in space and…
We develop an efficient $hp$-finite element method for piecewise-smooth differential equations with periodic boundary conditions, using orthogonal polynomials defined on circular arcs. The operators derived from this basis are banded and…
In the present work, we investigate the computational efficiency afforded by higher-order finite-element discretization of the saddle-point formulation of orbital-free density functional theory. We first investigate the robustness of viable…
The finite element method is used to approximately solve boundary value problems for differential equations. The method discretises the parameter space and finds an approximate solution by solving a large system of linear equations. Here we…
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…
This article is concerned with the numerical solution of convex variational problems. More precisely, we develop an iterative minimisation technique which allows for the successive enrichment of an underlying discrete approximation space in…
The first part of the cumulative thesis contains the numerical analysis of different $hp$-finite element discretizations related to two different weak formulations of a model problem in elastoplasticity with linearly kinematic hardening.…