Related papers: Fitted Finite Volume Method for a Generalized Blac…
Convergence results are shown for full discretizations of quasilinear parabolic partial differential equations on evolving surfaces. As a semidiscretization in space the evolving surface finite element method is considered, using a…
We propose consistent locally stabilized, conforming finite element schemes on completely unstructured simplicial space-time meshes for the numerical solution of non-autonomous parabolic evolution problems under the assumption of maximal…
In this paper, the generalized finite element method (GFEM) for solving second order elliptic equations with rough coefficients is studied. New optimal local approximation spaces for GFEMs based on local eigenvalue problems involving a…
Since early publications in the late 1980s and early 1990s, the finite volume method has been shown suitable for solid mechanics analyses. At present, there are several flavours of the method, which can be classified in a variety of ways,…
In this paper, a semi-discrete spatial finite volume (FV) method is proposed and analyzed for approximating solutions of anomalous subdiffusion equations involving a temporal fractional derivative of order $\alpha \in (0,1)$ in a…
We present a new technique to apply finite element methods to partial differential equations over curved domains. A change of variables along a coordinate transformation satisfying only low regularity assumptions can translate a Poisson…
This paper is devoted to the numerical validation of an explicit finite-difference scheme for the integration in time of Maxwell's equations in terms of the sole electric field, using standard linear finite elements for the space…
In this article, we provide a numerical method based on fitted finite volume method to approximate the Hamilton-Jacobi-Bellman (HJB) equation coming from stochastic optimal control problems. The computational challenge is due to the nature…
We consider an initial- and Dirichlet boundary- value problem for a linear Cahn-Hilliard-Cook equation, in one space dimension, forced by the space derivative of a space-time white noise. First, we propose an approximate regularized…
We consider the time-dependent Gross-Pitaevskii equation describing the dynamics of rotating Bose-Einstein condensates and its discretization with the finite element method. We analyze a mass conserving Crank-Nicolson-type discretization…
The presence of corners in the computational domain, in general, reduces the regularity of solutions of parabolic problems and diminishes the convergence properties of the finite element approximation introducing a so-called "pollution…
In this paper we focus on the subdiffusive Black Scholes model. The main part of our work consists of the finite difference method as a numerical approach to the option pricing in the considered model. We derive the governing fractional…
We propose and analyse a new type of fully discrete finite element approximation of a class of linear stochastic parabolic evolution equations with additive noise. Our discretization differs from previous ones in that we use a finite…
We propose and analyze a general framework for space-time finite element methods that is based on least-squares finite element methods for solving a first-order reformulation of the thick parabolic obstacle problem. Discretizations based on…
We consider locally stabilized, conforming finite element schemes on completely unstructured simplicial space-time meshes for the numerical solution of parabolic initial-boundary value problems with variable, possibly discontinuous in space…
The numerical solution of a nonlinear and space-fractional anti-diffusive equation used to model dune morphodynamics is considered. Spatial discretization is effected using a finite element method whereas the Crank-Nicolson scheme is used…
This work generalizes the subdiffusive Black-Scholes model by introducing the variable exponent in order to provide adequate descriptions for the option pricing, where the variable exponent may account for the variation of the memory…
We adapt the Gradient Discretisation Method (GDM), originally designed for elliptic and parabolic partial differential equations, to the case of a linear scalar hyperbolic equations. This enables the simultaneous design and convergence…
Numerical approximation of a stochastic partial integro-differential equation driven by a space- time white noise is studied by truncating a series representation of the noise, with finite element method for spatial discretization and…
In this paper we formulate and analyze a space-time finite element method for the numerical simulation of rotating electric machines where the finite element mesh is fixed in space-time domain. Based on the Babu\v{s}ka--Ne\v{c}as theory we…