The main result of this paper is a pointwise estimate for
the space time gradients of a temperature on a cylindrical
domain in terms of an iteration of two maximal operators. The
result is an extension to the parabolic setting…

We introduce a novel computational method for a Mumford-Shah functional, which decomposes a given image into smooth regions separated by closed curves. Casting this as a shape optimization problem, we develop a gradient descent approach at the continuous level that…

Abstract: Surface diffusion is a (4th order highly nonlinear) geometric driven motion of a surface with normal velocity proportional to the surface Laplacian of mean curvature. We present a novel variational formulation for graphs and derive a priori error estimates…

We introduce and study an adaptive finite element method for the Stokes system based on an Uzawa outer iteration to update the pressure and an elliptic adaptive inner iteration for velocity. We show linear convergence in terms of the outer…

Data oscillation is intrinsic information missed by the averaging process associated with finite element methods (FEM) regardless of quadrature. Ensuring a reduction rate of data oscillation, together with an error reduction based on a posteriori error estimators, we construct a…

In this work, transient free surface flows of a viscous incompressible fluid are numerically solved through parallel computation. Transient free surface flows are boundary-value problems of moving type that involve geometrical non-linearities. In contrast to more conventional CFD problems, the…

Mesh motion strategy is one of the key points in many
fluid-structure interaction (FSI) problems. Due to the increasing
application of FSI to solve the current challenging engineering
problems this topic has deserved a highlight interest. There are
several different…

A standard engineering procedure for approximating the solutions of an infinite-dimensional inverse problem of the form Ax = y, where A is a given compact linear operator on a Hilbert space X and y is the given data, is to…

Two-fluid models are central to the simulation of transport
processes in two-phase homogenized systems. Even though this physical
model has been widely accepted, an inherently non-hyperbolic and
non-conservative ill-posed problem arises from the mathematical point
of view. It has been…