We derive a posteriori error estimates for the (stopped) weak Euler method to discretize SDE
systems which emerge from the probabilistic reformulation of elliptic and parabolic (initial) …

Presenting systems of differential equations in the form of diagrams has become common in
certain parts of physics, especially electromagnetism and computational physics. In this …

In this paper we shall be concerned with Prandtl's equations with incompatible data, ie with
initial data that, in general, do not fulfil the boundary conditions imposed on the solution …

This paper considers the Navier–Stokes equations in the half plane with Euler-type initial
conditions, ie, initial conditions with a non-zero tangential component at the boundary …

Using the unified transform method we characterize the behavior of the solutions of linear
evolution partial differential equations on the half line in the presence of discontinuous initial …

Numerical approximations to the solutions of three different problem classes of singularly
perturbed parabolic reaction–diffusion problems, each with a discontinuity in the boundary …

We consider the Navier-Stokes equations of an incompressible fluid in a three dimensional
curved domain with permeable walls in the limit of small viscosity. Using a curvilinear …

On the Prandtl Boundary Layer Equations in Presence of Corner Singularities | SpringerLink
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The incompatibilities between the initial and boundary data will cause singularities at the
time-space corners, which in turn adversely affect the accuracy of the numerical schemes …

The objective of this thesis is the efficient approximation of high-dimensional stochastic
differential equations (SDE's) via newly developed, theoretical-based adaptive methods …