Related papers: Adaptive wavelet-based method for simulation of el…
The weak Galerkin (WG) finite element method is an effective and flexible general numerical technique for solving partial differential equations. It is a natural extension of the classic conforming finite element method for discontinuous…
Reduced-order models were derived for plane Couette flow using Galerkin projection, with orthonormal basis functions taken as the leading controllability modes of the linearised Navier-Stokes system for a few low wavenumbers. Resulting…
The representation of discrete, compact wavelet transformations (WTs) as circuits of local unitary gates is discussed. We employ a similar formalism as used in the multi-scale representation of quantum many-body wavefunctions using unitary…
This paper presents a new weak Galerkin (WG) method for elliptic interface problems on general curved polygonal partitions. The method's key innovation lies in its ability to transform the complex interface jump condition into a more…
We consider a distributed optimal control problem governed by an elliptic PDE, and propose an embedded discontinuous Galerkin (EDG) method to approximate the solution. We derive optimal a priori error estimates for the state, dual state,…
In this work we derive and analyze variational integrators of higher order for the structure-preserving simulation of mechanical systems. The construction is based on a space of polynomials together with Gauss and Lobatto quadrature rules…
This paper presents a high-order discontinuous Galerkin (DG) scheme for the simulation of wave propagation through coupled elastic-acoustic media. We use a first-order stress-velocity formulation, and derive a simple upwind-like numerical…
Motivated by considering partial differential equations arising from conservation laws posed on evolving surfaces, a new numerical method for an advection problem is developed and simple numerical tests are performed. The method is based on…
Graph-based models require aggregating information in the graph from neighbourhoods of different sizes. In particular, when the data exhibit varying levels of smoothness on the graph, a multi-scale approach is required to capture the…
The novel idea of weak Galerkin (WG) finite element methods is on the use of weak functions and their weak derivatives defined as distributions. Weak functions and weak derivatives can be approximated by polynomials with various degrees.…
We consider problems related to initial meshing and adaptive mesh refinement for the electromagnetic simulation of various structures. The quality of the initial mesh and the performance of the adaptive refinement are of great importance…
We use the ideas of goal-oriented error estimation and adaptivity to design and implement an efficient adaptive algorithm for approximating linear quantities of interest derived from solutions to elliptic partial differential equations…
In this paper, a new strategy for a sub-element based shock capturing for discontinuous Galerkin (DG) approximations is presented. The idea is to interpret a DG element as a collection of data and construct a hierarchy of low to high order…
We introduce a very weak space-time variational formulation for the wave equation, prove its well-posedness (even in the case of minimal regularity) and optimal inf-sup stability. Then, we introduce a tensor product-style space-time…
In this paper, we develop an adaptive multiresolution discontinuous Galerkin (DG) scheme for time-dependent transport equations in multi-dimensions. The method is constructed using multiwavlelets on tensorized nested grids. Adaptivity is…
Error estimates are proved for finite element approximations to the solution of second-order hyperbolic partial differential equations with coefficients varying in both space and time. Optimal rates of convergence in the energy norm are…
To investigate gauge theories with near-term quantum computers warrants exploration of nontraditional quantum simulators to find resource-efficient simulation protocols and ultimately access exotic features of different field theories,…
We design an adaptive virtual element method (AVEM) of lowest order over triangular meshes with hanging nodes in 2d, which are treated as polygons. AVEM hinges on the stabilization-free a posteriori error estimators recently derived in [8].…
Waves are all around us--be it in the form of sound, electromagnetic radiation, water waves, or earthquakes. Their study is an important basic tool across engineering and science disciplines. Every wave solver serving the computational…
This work is devoted to the study of a posteriori error estimation and adaptivity in parabolic problems with a particular focus on spatial discontinuous Galerkin (dG) discretisations. We begin by deriving an a posteriori error estimator for…