Related papers: Trace inequalities for piecewise $W^{1,p}$ functio…
In this paper we analyse the convergence properties of V-cycle multigrid algorithms for the numerical solution of the linear system of equations arising from discontinuous Galerkin discretization of second-order elliptic partial…
The aim of this paper is to obtain some generalized weighted Ostrowski inequalities for differentiable mappings. Some well known inequalities can be derived as special cases of the inequalities obtained here. In addition, perturbed…
We introduce a space-time Trefftz discontinuous Galerkin method for the first-order transient acoustic wave equations in arbitrary space dimensions, extending the one dimensional scheme of Kretzschmar et al. (2016, IMA J. Numer. Anal., 36,…
We introduce an $hp$-version symmetric interior penalty discontinuous Galerkin finite element method (DGFEM) for the numerical approximation of the biharmonic equation on general computational meshes consisting of polygonal/polyhedral…
In this paper, we study the relations between trace inequalities(Sobolev and Moser-Trudinger type), isocapacitary inequalities and the regularity of the complex Hessian and Monge-Amp\`ere equations with respect to a general positive Borel…
We establish sharp trace- and Korn-type inequalities that involve vectorial differential operators, the focus being on situations where global singular integral estimates are not available. Starting from a novel approach to sharp Besov…
The main goal of this paper is to give a complete proof of the trace theorem for Besov-type spaces of generalized smoothness associated with complete Bernstein functions satisfying certain scaling conditions on $d$-sets $D\subset\mathbb…
In this paper we characterize the trace spaces of a class of weighted function spaces of intersection type with mixed regularities. To a large extent we can overcome the difficulty of mixed scales by employing a microscopic improvement in…
In metric measure spaces, we study boundary traces of BV functions in domains equipped with a doubling measure and supporting a Poincar\'e inequality, but possibly having a very large and irregular boundary. We show that the trace exists in…
The dynamics of a tracer particle in a stationary driven granular gas is investigated. We show how to transform the linear Boltzmann equation describing the dynamics of the tracer into a master equation for a continuous Markov process. The…
This work introduces a novel Trefftz Continuous Galerkin (TCG) method for 2D Helmholtz problems based on evanescent plane waves (EPWs). We construct a new globally-conforming discrete space, departing from standard discontinuous Trefftz…
Matrices and more generally multidimensional arrays, form the backbone of computational studies. In this paper we demonstrate increases in computational efficiency by performing partial-tracing/tensor-contractions on sparse-arrays. It was…
We consider the completely positive discretizations of fractional ordinary differential equations (FODEs) on nonuniform meshes. Making use of the resolvents for nonuniform meshes, we first establish comparison principles for the…
We examine a variational multiscale method in which the unresolved fine-scales are approximated element-wise using a discontinuous Galerkin method. We establish stability and convergence results for the methodology as applied to the scalar…
We provide a unified method to study the adjacency matrices of regular graphs (including infinite ones) using holomorphic functional calculus. By applying this calculus on a specific ellipse that contains the spectrum, we derive an…
Let $(\operatorname{X},\operatorname{d},\mu)$ be a metric measure space with uniformly locally doubling measure $\mu$. Given $p \in (1,\infty)$, assume that $(\operatorname{X},\operatorname{d},\mu)$ supports a weak local $(1,p)$-Poincar\'e…
In this paper, we revisit Korn's inequality for the piecewise $H^1$ space based on general polygonal or polyhedral decompositions of the domain. Our Korn's inequality is expressed with minimal jump terms. These minimal jump terms are…
We present a novel Discontinuous Galerkin Finite Element Method for wave propagation problems. The method employs space-time Trefftz-type basis functions that satisfy the underlying partial differential equations and the respective…
An algorithm for solving nonconvex smooth optimization problems is proposed, analyzed, and tested. The algorithm is an extension of the Trust Region Algorithm with Contractions and Expansions (TRACE) [Math. Prog. 162(1):132, 2017]. In…
The novel idea of weak Galerkin (WG) finite element methods is on the use of weak functions and their weak derivatives defined as distributions. Weak functions and weak derivatives can be approximated by polynomials with various degrees.…