相关论文: Resolvent estimates and numerical implementation f…

In this work, a complete error analysis is presented for fully discrete solutions of the subdiffusion equation with a time-dependent diffusion coefficient, obtained by the Galerkin finite element method with conforming piecewise linear…

We introduce a family of proximal discontinuous Galerkin methods for variational inequalities, focusing on the obstacle problem as a didactic example. Each member of this family is born from applying a different well-known nonconforming…

This paper analyzes the error estimates of the hybridizable discontinuous Galerkin (HDG) method for the Helmholtz equation with high wave number in two and three dimensions. The approximation piecewise polynomial spaces we deal with are of…

We introduce a family of mixed methods and discontinuous Galerkin discretisations designed to numerically solve the Oseen equations written in terms of velocity, vorticity, and Bernoulli pressure. The unique solvability of the continuous…

We present and analyze a discontinuous Galerkin method for the numerical modeling of the non-linear fully-coupled thermo-hydro-mechanic problem. We propose a high-order symmetric weighted interior penalty scheme that supports general…

We introduce a finite element method for numerical upscaling of second order elliptic equations with highly heterogeneous coefficients. The method is based on a mixed formulation of the problem and the concepts of the domain decomposition…

We study the averaging of fronts moving with positive oscillatory normal velocity, which is periodic in space and stationary ergodic in time. The problem can be reformulated as the homogenization of coercive level set Hamilton-Jacobi…

We consider a class of elasticity equations in ${\mathbb R}^d$ whose elastic moduli depend on $n$ separated microscopic scales, are random and expressed as a linear expansion of a countable sequence of random variables which are…

We propose an efficient variant of a primal Discontinuous Galerkin method with interior penalty for the second order elliptic equations on very general meshes (polytopes with eventually curved boundaries). Efficiency, especially when higher…

We introduce a new Partition of Unity Method for the numerical homogenization of elliptic partial differential equations with arbitrarily rough coefficients. We do not restrict to a particular ansatz space or the existence of a finite…

In this paper we develop an adaptive procedure for the numerical solution of semilinear parabolic problems, with possible singular perturbations. Our approach combines a linearization technique using Newton's method with an adaptive…

When homogenizing elliptic partial differential equations, the so-called corrector problem is pivotal to compute the macroscale effective coefficients from the microscale information. To solve this corrector problem in the periodic setting,…

Numerical homogenization, i.e. the finite-dimensional approximation of solution spaces of PDEs with arbitrary rough coefficients, requires the identification of accurate basis elements. These basis elements are oftentimes found after a…

This paper is devoted to the numerical analysis of a control constrained distributed optimal control problem subject to a time fractional diffusion equation with non-smooth initial data. The solutions of state and co-state are decomposed…

Homogenization of a thin micro-structure yields effective jump conditions that incorporate the geometrical features of the scatterers. These jump conditions apply across a thin but nonzero thickness interface whose interior is disregarded.…

In this work numerical methods for solving Einstein's equations are developed and applied to the study of inhomogeneous cosmological models. A two-dimensional computer code is described which implements two advanced numerical methods:…

The discontinuous Galerkin dG method provides a robust and flexible technique for the time integration of fractional diffusion problems. However, a practical implementation uses coefficients defined by integrals that are not easily…

This article is concerned with numerical methods to approximate effective coefficients in stochastic homogenization of discrete linear elliptic equations, and their numerical analysis --- which has been made possible by recent contributions…

We present and analyze a hybridizable discontinuous Galerkin (HDG) method for the time-harmonic Maxwell equations. The divergence-free condition is enforced on the electric field, then a Lagrange multiplier is introduced, and the problem…

In this work, we study a system of coupled Cahn-Hilliard equations describing the phase separation of a copolymer and a homopolymer blend. The numerical methods we propose are based on suitable combinations of existing schemes for the…