相关论文: Building Space-Time Meshes over Arbitrary Spatial …

We present a class of spline finite element methods for time-domain wave propagation which are particularly amenable to explicit time-stepping. The proposed methods utilize a discontinuous Galerkin discretization to enforce continuity of…

We propose a graph-based sweep algorithm for solving the steady state, mono-energetic discrete ordinates on meshes of high-order curved mesh elements. Our spatial discretization consists of arbitrarily high-order discontinuous Galerkin…

We consider the Weak Galerkin finite element approximation of the Singularly Perturbed Biharmonic elliptic problem on a unit square domain with clamped boundary conditions. Shishkin mesh is used for domain discretization as the solution…

In this article, we propose novel boundary treatment algorithms to avoid order reduction when implicit-explicit Runge-Kutta time discretization is used for solving convection-diffusion-reaction problems with time-dependent Di\-richlet…

The aim of this paper is to analyze a mixed discontinuous Galerkin discretization of the time-harmonic elasticity problem. The symmetry of the Cauchy stress tensor is imposed weakly, as in the traditional dual-mixed setting. We show that…

A new discontinuous Galerkin finite element method for the Stokes equations is developed in the primary velocity-pressure formulation. This method employs discontinuous polynomials for both velocity and pressure on general…

In this paper we develop a class of efficient Galerkin boundary element methods for the solution of two-dimensional exterior single-scattering problems. Our approach is based upon construction of Galerkin approximation spaces confined to…

In this paper, we analyze and provide numerical illustrations for a moving finite element method applied to convection-dominated, time-dependent partial differential equations. We follow a method of lines approach and utilize an underlying…

This study presents novel strategies for improving the node-level performance of matrix-free evaluation of continuous and discontinuous Galerkin spatial discretizations on unstructured tetrahedral grids. In our approach the underlying…

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 we study the finite element approximation of systems of second-order nonlinear hyperbolic equations. The proposed numerical method combines a $hp$-version discontinuous Galerkin finite element approximation in the time…

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…

This paper presents a fast an robust mesh generation procedure that is able to generate meshes of the earth system (ocean and continent) in matters of seconds. Our algorithm takes as input a standard shape-file i.e. geospatial vector data…

In this paper we present a novel arbitrary high order accurate discontinuous Galerkin (DG) finite element method on space-time adaptive Cartesian meshes (AMR) for hyperbolic conservation laws in multiple space dimensions, using a high order…

Mesh generation remains a key technology in many areas where numerical simulations are required. As numerical algorithms become more efficient and computers become more powerful, the percentage of time devoted to mesh generation becomes…

We present a method to extend the finite element library FEniCS to solve problems with domains in dimensions above three by constructing tensor product finite elements. This methodology only requires that the high dimensional domain is…

We present and analyze a new space-time finite element method for the solution of neural field equations with transmission delays. The numerical treatment of these systems is rare in the literature and currently has several restrictions on…

The conformal formulation of the Einstein constraint equations is first reviewed, and we then consider the design, analysis, and implementation of adaptive multilevel finite element-type numerical methods for the resulting coupled nonlinear…

Multi-adaptive Galerkin methods are extensions of the standard continuous and discontinuous Galerkin methods for the numerical solution of initial value problems for ordinary or partial differential equations. In particular, the…

In this paper, a space-time discontinuous Galerkin finite element method for distributed optimal control problems governed by unsteady diffusion-convection-reaction equations with control constraints is studied. Time discretization is…