Related papers: Numerical approximation of linear parabolic evolut…

In this paper we consider the numerical approximation of the incompressible surface Navier--Stokes equations on an evolving surface. For the discrete representation of the moving surface we use parametric finite elements of degree $\ell…

Extending results of Pardoux and Peng and Hu and Peng, we prove well-posedness results for backward stochastic evolution equations in UMD Banach spaces.

We present a general method of solving the Cauchy problem for a linear parabolic partial differential equation of evolution type with variable coefficients and demonstrate it on the equation with derivatives of orders two, one and zero. The…

We present a numerical method for approximating the solutions of degenerate parabolic equations with a formal gradient flow structure. The numerical method we propose preserves at the discrete level the formal gradient flow structure,…

For a parabolic surface partial differential equation coupled to surface evolution, convergence of the spatial semidiscretization is studied in this paper. The velocity of the evolving surface is not given explicitly, but depends on the…

The subject of this work is an adaptive stochastic Galerkin finite element method for parametric or random elliptic partial differential equations, which generates sparse product polynomial expansions with respect to the parametric…

In this paper we consider approximations of Neumann problems for the integral fractional Laplacian by continuous, piecewise linear finite elements. We analyze the weak formulation of such problems, including their well-posedness and…

We develop a unified theory for continuous in time finite element discretisations of partial differential equations posed in evolving domains including the consideration of equations posed on evolving surfaces and bulk domains as well…

In this work, we investigate the numerical approximation of the second order non-autonomous semilnear parabolic partial differential equation (PDE) using the finite element method. To the best of our knowledge, only the linear case is…

In this paper we consider convergence of approximate solutions of conservation laws. We start with an overview over the historical developments since the 1950s, and the analytical tools used in this context. Then we present some of our own…

We show that the there exists an algebraic rate of convergence of solutions of finite-difference approximations for uniformly elliptic Isaacs in smooth bounded domains.

In this paper, we study finite dimensional approximations of Kohn-Sham models, which are widely used in electronic structure calculations. We prove the convergence of the finite dimensional approximations and derive the a priori error…

We study the rate of convergence of an explicit and an implicit-explicit finite difference scheme for linear stochastic integro-differential equations of parabolic type arising in non-linear filtering of jump-diffusion processes. We show…

We obtain sharp approximation results for into nearisometries between Lp spaces and nearisometries into a Hilbert space. Our main theorem is the optimal approximation result for nearsurjective nearisometries between general Banach spaces.

We derive global analytic representations of fundamental solutions for a class of linear parabolic systems with full coupling of first order derivative terms where coefficient may depend on space and time. Pointwise convergence of the…

We consider an evolutionary problem with rapidly oscillating coefficients. This causes the problem to change frequently between a parabolic and an hyperbolic state. We prove convergence of the homogenisation process in the unit square and…

We provide global gradient estimates for solutions to a general type of nonlinear parabolic equations, possibly in a Riemannian geometry setting. Our result is new in comparison with the existing ones in the literature, in light of the…

In this paper, we study the existence of the random approximations and fixed points for random almost lower semicontinuous operators defined on finite dimensional Banach spaces, which in addition, are condensing or 1-set-contractive. Our…

This work is devoted to the study of a class of linear time-inhomogeneous evolution equations in a scale of Banach spaces. Existence, uniquenss and stability for classical solutions is provided. We study also the associated dual Cauchy…

The aim of this work is to show an abstract framework to analyze the numerical approximation for a family of linear degenerate parabolic mixed equations by using a finite element method in space and a Backward-Euler scheme in time. We…