Related papers: A second-order face-centred finite volume method o…
Interface problems have long been a major focus of scientific computing, leading to the development of various numerical methods. Traditional mesh-based methods often employ time-consuming body-fitted meshes with standard discretization…
A new higher-order accurate method is proposed that combines the advantages of the classical $p$-version of the FEM on body-fitted meshes with embedded domain methods. A background mesh composed by higher-order Lagrange elements is used.…
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…
In this work, we introduce new families of nonconforming approximation methods for reconstructing functions on general polygonal meshes. These methods are defined using degrees of freedom based on weighted moments of orthogonal polynomials…
A new discretisation scheme for the gradient operator, suitable for use in second-order accurate Finite Volume Methods (FVMs), is proposed. The derivation of this scheme, which we call the Taylor-Gauss (TG) gradient, is similar to that of…
Muscle-based systems have the potential to provide both anatomical accuracy and semantic interpretability as compared to blendshape models; however, a lack of expressivity and differentiability has limited their impact. Thus, we propose…
Adaptive meshes have the potential to improve the accuracy and efficiency of atmospheric modelling by increasing resolution where it is most needed. Mesh re-distribution, or r-adaptivity, adapts by moving the mesh without changing the…
An adaptive moving mesh finite element method is studied for the numerical solution of the porous medium equation with and without variable exponents and absorption. The method is based on the so-called moving mesh partial differential…
A novel finite element framework is proposed for the numerical simulation of two phase flows with surface tension. The Level-Set (LS) method with piece-wise quadratic (P2) interpolation for the liquid-gas interface is used in order to reach…
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 propose an upwind finite volume method for a system of two kinetic equations in one dimension that are coupled through nonlocal interaction terms. These cross-interaction systems were recently obtained as the mean-field limit of a…
In this paper, we propose a multilevel stochastic framework for the solution of nonconvex unconstrained optimization problems. The proposed approach uses random regularized first-order models that exploit an available hierarchical…
A face-centred finite volume (FCFV) method is proposed for the linear elasticity equation. The FCFV is a mixed hybrid formulation, featuring a system of first-order equations, that defines the unknowns on the faces (edges in two dimensions)…
Efforts to achieve better accuracy in numerical relativity have so far focused either on implementing second order accurate adaptive mesh refinement or on defining higher order accurate differences and update schemes. Here, we argue for the…
We propose a multiscale approach for an elliptic multiscale setting with general unstructured diffusion coefficients that is able to achieve high-order convergence rates with respect to the mesh parameter and the polynomial degree. The…
The high-order numerical analysis for fractional Laplacian via the Riesz fractional derivative, under the low regularity solution, has presented significant challenges in the past decades. To fill in this gap, we design a grid mapping…
A novel fifth-order compact gas-kinetic scheme is developed for high-resolution simulation of compressible flows on structured meshes. Its accuracy relies on a new multidimensional fifth-order compact reconstruction that uses line-averaged…
Mesh adaption procedures for finite element approximation allows one to adapt the resolution, by local refinement in the regions of strong variation of the function of interest. This procedure plays a key role in numerous applications of…
Stokes flow equations have been implemented successfully in practice for simulating problems with moving interfaces. Though computational methods produce accurate solutions and numerical convergence can be demonstrated using a resolution…
Finite element methods based on cut-cells are becoming increasingly popular because of their advantages over formulations based on body-fitted meshes for problems with moving interfaces. In such methods, the cells (or elements) which are…