Related papers: A finite element data assimilation method for the …
Despite its numerical challenges, finite element method is used to compute viscous fluid flow. A consensus on the cause of numerical problems has been reached; however, general algorithms---allowing a robust and accurate simulation for any…
We develop a fully discrete scheme for time-fractional diffusion equations by using a finite difference method in time and a finite element method in space. The fractional derivatives are used in Caputo sense. Stability and error estimates…
A high order cut finite element method is formulated for solving the elastic wave equation. Both a single domain problem and an interface problem are treated. The boundary or interface are allowed to cut through the background mesh. To…
Structured Finite Element Methods (FEMs) based on low-rank approximation in the form of the so-called Quantized Tensor Train (QTT) decomposition (QTT-FEM) have been proposed and extensively studied in the case of elliptic equations. In this…
A new numerical method is presented for solving the rotating shallow water equations on a rotating sphere using quasi-uniform polygonal meshes. The method uses special families of finite element function spaces to mimic key mathematical…
We present and analyze two stabilized finite element methods for solving numerically the Poisson--Nernst--Planck equations. The stabilization we consider is carried out by using a shock detector and a discrete graph Laplacian operator for…
We consider the scattering of acoustic perturbations in a presence of a flow. We suppose that the space can be split into a zone where the flow is uniform and a zone where the flow is potential. In the first zone, we apply a Prandtl-Glauert…
Adaptive Finite Element Method (adaptivity) is known to be an effective numerical tool for some ill-posed problems. The key advantage of the adaptivity is the image improvement with local mesh refinements. A rigorous proof of this property…
In this paper, a symmetrized two-scale finite element method is proposed for a class of partial differential equations with symmetric solutions. With this method, the finite element approximation on a fine tensor product grid is reduced to…
A proof of convergence is given for a novel evolving surface finite element semi-discretization of Willmore flow of closed two-dimensional surfaces, and also of surface diffusion flow. The numerical method proposed and studied here…
A precise domain triangulation is recognized as indispensable for the accurate numerical approximation of differential operators within collocation methods, leading to a substantial reduction in discretization errors. An efficient finite…
Approximated numerical techniques, for the solution of the elastic wave scattering problem over semi-infinite domains are reviewed. The approximations involve the representation of the half-space by a boundary condition described in terms…
This paper develops a smoothing-based postprocessing method for superconvergence in finite element methods. The method applies a few smoothing iterations, such as damped Jacobi, Gauss-Seidel, or conjugate gradient, with initial guess being…
We consider a space-time variational formulation of the second-order wave equation, where integration by parts is also applied with respect to the time variable. Conforming tensor-product finite element discretisations with piecewise…
This paper focuses on identifying the cause and proposing a remedy for the problem of spurious pressure oscillations in a sharp-interface immersed boundary finite element method for incompressible flow problems in moving domains. The…
We construct a structure preserving non-conforming finite element approximation scheme for the bi-harmonic wave maps into spheres equation. It satisfies a discrete energy law and preserves the non-convex sphere constraint of the continuous…
A proof of convergence is given for semi- and full discretizations of mean curvature flow of closed two-dimensional surfaces. The numerical method proposed and studied here combines evolving finite elements, whose nodes determine the…
A numerical scheme is presented for approximating fractional order Poisson problems in two and three dimensions. The scheme is based on reformulating the original problem posed over $\Omega$ on the extruded domain…
Fitted finite element methods are constructed for a singularly perturbed convection-diffusion problem in two space dimensions. Exponential splines as basis functions are combined with Shishkin meshes to obtain a stable parameter-uniform…
A high-frequency recovered fully discrete low-regularity integrator is constructed to approximate rough and possibly discontinuous solutions of the semilinear wave equation. The proposed method, with high-frequency recovery techniques, can…