This paper introduces a G space theory and a weakened weak form (W2) using the generalized gradient smoothing technique for a unified formulation of a wide class of compatible and incompatible methods. The W2 formulation works for both finite element method settings and mesh-free settings, and W2 models can have special properties including softened behavior, upper bounds and ultra accuracy. Pa...

This paper is devoted to the mathematical analysis of a degenerate nonlinear parabolic equation. This kind of equations stems either from the modeling of a compressible two phase flow in porous media or from the modeling of a chemotaxis-fluid process. In the degenerate equation, the strong nonlinearities are technically difficult to be controlled by the degenerate dissipative term because the e...

where the unknown f(t, x, v) is a nonnegative integrable function standing for the density of particles in phase space : time t ≥ 0, position x ∈ R, velocity v ∈ R, n ≥ 2. More precisely, this first part is devoted to some properties linked with the operator from (1.13) below, which is linked with one possible weak formulation of Boltzmann equation (1.1). On the right hand side of (1.1), Q is t...

A spacetime discontinuous Petrov-Galerkin (DPG) method for the linear wave equation is presented. This method is based on a weak formulation that uses a broken graph space. The wellposedness of this formulation is established using a previously presented abstract framework. One of the main tasks in the verification of the conditions of this framework is proving a density result. This is done in...

We propose Dirichlet Process mixtures of Generalized Linear Models (DP-GLM), a new class of methods for nonparametric regression. Given a data set of input-response pairs, the DP-GLM produces a global model of the joint distribution through a mixture of local generalized linear models. DP-GLMs allow both continuous and categorical inputs, and can model the same class of responses that can be mo...

In this paper, we propose an alternative notion, called weak forgetting, of forgetting a set of predicates in a first-order theory. One important feature of this new notion is that the result of weak forgetting is always first-order expressible. In contrast, this is not the case for the traditional notion of forgetting, called strong forgetting, introduced by Lin and Reiter. As a consequence, t...

In this research note we provide a variational basis for the optimal artificial diffusion method, which has been a cornerstone in developing many stabilized methods. The optimal artificial diffusion method produces exact nodal solutions when applied to one-dimensional problems with constant coefficients and forcing function. We first present a variational principle for a multi-dimensional advec...

Within the framework of elastoplastic analysis the focus is set on the rate-independent evolutionary problem with general hardening whose material characteristics are assumed to be uncertain. These processes are described via a stochastic convex energy function and evolution equations for internal variables. Computationally such posed problem reduces to the stochastic minimisation of smooth con...

We present novel enhanced finite element methods for the Darcy problem starting from the non stable continuous P1/P0 finite element space enriched with multiscale functions. The methods are derived in a Petrov-Galerkin framework where both velocity and pressure trial spaces are enriched with functions based on residuals of the strong equations in each element and edge partition. The strategy le...

*Correspondence: [email protected] 1School of Mathematics and Physics, China University of Geosciences, Lumo 388, Wuhan, 430074, China Full list of author information is available at the end of the article Abstract In this paper we start by giving a new definition of weak Caputo derivative in the sense of distributions, and we give a variational formulation to a fractional diffusion equa...