Related papers: A Space-Time Cut Finite Element Method with quadra…
In this paper, we propose a variationally consistent technique for decreasing the maximum eigenfrequencies of structural dynamics related finite element formulations. Our approach is based on adding a symmetric positive-definite term to the…
The paper studies a finite element method for computing transport and diffusion along evolving surfaces. The method does not require a parametrization of a surface or an extension of a PDE from a surface into a bulk outer domain. The…
We consider the null controllability problem for the wave equation, and analyse a stabilized finite element method formulated on a global, unstructured spacetime mesh. We prove error estimates for the approximate control given by the…
Immersed finite element methods provide a convenient analysis framework for problems involving geometrically complex domains, such as those found in topology optimization and microstructures for engineered materials. However, their…
Numerical simulations of brittle fracture using phase-field approaches often employ a discrete approximation framework that applies the same order of interpolation for the displacement and phase-field variables. Most common is to use linear…
We present a novel framework based on semi-bounded spatial operators for analyzing and discretizing initial boundary value problems on moving and deforming domains. This development extends an existing framework for well-posed problems and…
In contrast with the diffusion equation which smoothens the initial data to $C^\infty$ for $t>0$ (away from the corners/edges of the domain), the subdiffusion equation only exhibits limited spatial regularity. As a result, one generally…
In this paper, we propose a novel unstructured mesh control volume method to deal with the space fractional derivative on arbitrarily shaped convex domains, which to the best of our knowledge is a new contribution to the literature.…
We introduce an arbitrary order, stabilized finite element method for solving a unique continuation problem subject to the time-harmonic elastic wave equation with variable coefficients. Based on conditional stability estimates we prove…
In this work we study various continuous finite element discretization for two dimensional hyperbolic partial differential equations, varying the polynomial space (Lagrangian on equispaced, Lagrangian on quadrature points (Cubature) and…
We consider a space-time finite element method on fully unstructured simplicial meshes for optimal sparse control of semilinear parabolic equations. The objective is a combination of a standard quadratic tracking-type functional including a…
A finite element approach for approximating the solution of a mathematical model for the response of a penetrable, bounded object (obstacle) to the excitation by an external electromagnetic field is presented and investigated. The model…
In this paper, we investigate the combination of a linear continuous interior penalty type and a non-linear artificial diffusion stabilisation applied to the transport problem, based on continuous Galerkin finite elements in space. This…
This work introduces and analyzes a finite element scheme for evolution problems involving fractional-in-time and in-space differentiation operators up to order two. The left-sided fractional-order derivative in time we consider is employed…
Stabilization is a key dependability property for dealing with unanticipated transient faults, as it guarantees that even in the presence of such faults, the system will recover to states where it satisfies its specification. One of the…
In this work, we present scalable balancing domain decomposition by constraints methods for linear systems arising from arbitrary order edge finite element discretizations of multi-material and heterogeneous 3D problems. In order to enforce…
We present a fully discrete stability analysis of the domain-of-dependence stabilization for hyperbolic problems. The method aims to address issues caused by small cut cells by redistributing mass around the neighborhood of a small cut cell…
We consider a space-time variational formulation of the second-order wave equation, where integration by parts is also applied with respect to the time variable. Conforming tensor-product finite element discretisations with piecewise…
We present an efficient and robust numerical algorithm for solving the two-dimensional linear elasticity problem that combines the Quantized Tensor Train format and a domain partitioning strategy. This approach makes it possible to solve…
This paper constructs a predictor-corrector technique with orthogonal spline collocation finite element method for simulating a FitzHugh-Nagumo system subject to suitable initial and boundary conditions. The developed computational…