We use the local orthogonal decomposition technique introduced in Målqvist and Peterseim (Math Comput 83(290):2583-2603, 2014) to derive a generalized finite element method for linear and semilinear parabolic equations with spatial multiscale coefficients. We consider nonsmooth initial data and a backward Euler scheme for the temporal discretization. Optimal order convergence rate, depending on...

We study a discretization technique for the parabolic fractional obstacle problem in bounded domains. The fractional Laplacian is realized as the Dirichlet-to-Neumann map for a nonuniformly elliptic equation posed on a semi-infinite cylinder, which recasts our problem as a quasi-stationary elliptic variational inequality with a dynamic boundary condition. The rapid decay of the solution suggest...

Abstract. A new morphological multiscale method in 3D image processing is presented which combines the image processing methodology based on nonlinear diffusion equations and the theory of geometric evolution problems. Its aim is to smooth level sets of a 3D image while simultaneously preserving geometric features such as edges and corners on the level sets. This is obtained by an anisotropic c...

Abstract. A new morphological multiscale method in 3D image processing is presented which combines the image processing methodology based on nonlinear diffusion equations and the theory of geometric evolution problems. Its aim is to smooth level sets of a 3D image while simultaneously preserving geometric features such as edges and corners on the level sets. This is obtained by an anisotropic c...

We develop a family of Eulerian-Lagrangian localized adjoint methods for the solution of the initial-boundary value problems for rst-order advection-reaction equations on general multi-dimensional domains. Diierent tracking algorithms, including the Euler and Runge-Kutta algorithms, are used. The derived schemes naturally incorporate innow boundary conditions into their formulations and do not ...

In this paper,we consider theCOSmethod for pricing European andBermudan options under the stochastic alpha beta rho (SABR) model. In the COS pricing method, we make use of the characteristic function of the discrete forward process. We observe second-order convergence by using a second-order Taylor scheme in the discretization, or by using Richardson extrapolation in combination with a Euler–Ma...

In this work we consider a mathematical model for two-phase flow in porous media.The fluids are assumed immiscible and incompressible and the solid matrix non-deformable. The mathematical model for the two-phase flow is written in terms of the global pressure and a complementary pressure (obtained by using the Kirchhoff transformation) as primary unknowns. For the spatial discretization, finite...

This paper deals with a method for the numerical solution of parabolic initialboundary value problems in two-dimensional polygonal domains Ω which are allowed to be non-convex. The Nitsche finite element method (as a mortar method) is applied for the discretization in space, i.e. non-matching meshes are used. For the discretization in time, the backward Euler method is employed. The rate of con...

We present a numerical comparison of some time{stepping schemes for the discretization and solution of the nonstationary incompressible Navier{Stokes equations. The spatial discretization is by nonconforming quadrilateral nite elements which satisfy the LBB{condition. The major focus is on the diierences in accuracy and eeciency between the Backward Euler-, Crank{Nicolson-or Fractional{step{{sc...

We present and analyze a hybridizable discontinuous Galerkin (HDG) finite element method for the coupled Stokes–Biot problem. Of particular interest is that discrete velocities displacement are H(div)-conforming satisfy compressibility equations pointwise on elements. Furthermore, in incompressible limit, discretization strongly conservative. prove well-posedness of and, after combining HDG wit...