Related papers: Space-time least-squares finite elements for parab…
This paper is concerned with fully discrete finite element methods for approximating variational solutions of nonlinear stochastic elastic wave equations with multiplicative noise. A detailed analysis of the properties of the weak solution…
The aim of this paper is to develop stable and accurate numerical schemes for boundary integral formulations of the heat equation with Dirichlet boundary conditions. The accuracy of Galerkin discretisations for the resulting boundary…
Maximal regularity is a fundamental concept in the theory of partial differential equations. In this paper, we establish a fully discrete version of maximal regularity for a parabolic equation. We derive various stability results in…
We consider the numerical approximation of a continuum model of antiferromagnetic and ferrimagnetic materials. The state of the material is described in terms of two unit-length vector fields, which can be interpreted as the magnetizations…
We prove higher integrability up to the boundary for minimal p-weak upper gradients of parabolic quasiminimizers in metric measure spaces, related to the heat equation. We assume the underlying metric measure space to be equipped with a…
We establish a well-posedness and error-estimation framework that solves Hamilton-Jacobi equations by minimizing the least-squares residual of monotone finite-difference discretizations. This approach also applies naturally to second-order…
We present a weak finite element method for elliptic problems in one space dimension. Our analysis shows that this method has more advantages than the known weak Galerkin method proposed for multi-dimensional problems, for example, it has…
This paper presents a structure-preserving spatial discretization method for distributed parameter port-Hamiltonian systems. The class of considered systems are hyperbolic systems of two conservation laws in arbitrary spatial dimension and…
A concise Matlab implementation of a stable parallelizable space-time Petrov-Galerkin discretization for parabolic evolution equations is given. Emphasis is on reusability of spatial finite element codes.
For linear parabolic initial-boundary value problems with self-adjoint, time-homogeneous elliptic spatial operator in divergence form with Lipschitz-continuous coefficients, and for incompatible, time-analytic forcing term in…
It was recently observed that chiral two-body interactions can be efficiently represented using matrix factorization techniques such as the singular value decomposition. However, the exploitation of these low-rank structures in a few- or…
Time-dependent Maxwell's equations govern electromagnetics. Under certain conditions, we can rewrite these equations into a partial differential equation of second order, which in this case is the vectorial wave equation. For the vectorial…
We propose a new least squares finite element method to solve the Poisson equation. By using a piecewisely irrotational space to approximate the flux, we split the classical method into two sequential steps. The first step gives the…
In this paper, we propose a linearized finite element method (FEM) for solving the cubic nonlinear Schr\"{o}dinger equation with wave operator. In this method, a modified leap-frog scheme is applied for time discretization and a Galerkin…
We propose, analyze, and test new robust iterative solvers for systems of linear algebraic equations arising from the space-time finite element discretization of reduced optimality systems defining the approximate solution of hyperbolic…
We consider a space-time variational formulation of parabolic initial-boundary value problems in anisotropic Sobolev spaces in combination with a Hilbert-type transformation. This variational setting is the starting point for the space-time…
We develop multipoint stress mixed finite element methods for linear elasticity with weak stress symmetry on cuboid grids, which can be reduced to a symmetric and positive definite cell-centered system. The methods employ the lowest-order…
We study the time regularity of local weak solutions of the heat equation in the context of local regular symmetric Dirichlet spaces. Under two basic and rather minimal assumptions, namely, the existence of certain cut-off functions and a…
We investigate theoretically and numerically the use of the Least-Squares Finite-element method (LSFEM) to approach data-assimilation problems for the steady-state, incompressible Navier-Stokes equations. Our LSFEM discretization is based…
We develop a multipoint stress mixed finite element method for linear elasticity with weak stress symmetry on quadrilateral grids, which can be reduced to a symmetric and positive definite cell centered system. The method is developed on…