Spectral methods on triangles and other domains

High-Order Mixed Current Basis Functions for Electromagnetic Scattering of Curved Surfaces

Journal of Scientific Computing

On the Coupling of Local Discontinuous Galerkin and Conforming Finite Element Methods

Journal of Scientific Computing

Runge–Kutta Discontinuous Galerkin Methods for Convection-Dominated Problems

Journal of Scientific Computing

Nodal high-order methods on unstructured grids

Journal of Computational Physics

Jacobi approximations in non-uniformly Jacobi-weighted Sobolev spaces

Journal of Approximation Theory

Spectral element methods on triangles and quadrilaterals: comparisons and applications

Journal of Computational Physics

Algorithm 839: FIAT, a new paradigm for computing finite element basis functions

ACM Transactions on Mathematical Software (TOMS)

Discontinuous Galerkin Methods Applied to Shock and Blast Problems

Journal of Scientific Computing

Discontinuous Galerkin Spectral/hp Element Modelling of Dispersive Shallow Water Systems

Journal of Scientific Computing

A nodal triangle-based spectral element method for the shallow water equations on the sphere

Journal of Computational Physics

Improved Lebesgue constants on the triangle

Journal of Computational Physics

Discontinuous Galerkin methods applied to shock and blast problems

Journal of Scientific Computing

Discontinuous Galerkin spectral/hpelement modelling of dispersive shallow water systems

Journal of Scientific Computing

Spectral/hp discontinuous Galerkin methods for modelling 2D Boussinesq equations

Journal of Computational Physics

Spectral Element Methods on Unstructured Meshes: Comparisons and Recent Advances

Journal of Scientific Computing

High-order triangle-based discontinuous Galerkin methods for hyperbolic equations on a rotating sphere

Journal of Computational Physics

High-order discontinuous Galerkin methods using an hp-multigrid approach

Journal of Computational Physics

Optimizing FIAT with level 3 BLAS

ACM Transactions on Mathematical Software (TOMS)

Arbitrary high order non-oscillatory finite volume schemes on unstructured meshes for linear hyperbolic systems

Journal of Computational Physics

A spectral element least-squares formulation for incompressible Navier-Stokes flows using triangular nodal elements

Journal of Computational Physics

A high-order discontinuous Galerkin method for the unsteady incompressible Navier-Stokes equations

Journal of Computational Physics

Application of conservative residual distribution schemes to the solution of the shallow water equations on unstructured meshes

Journal of Computational Physics

Numerical simulation of optical coupling and light propagation in coupled optical resonators with size disorder

Applied Numerical Mathematics

Application of implicit-explicit high order Runge-Kutta methods to discontinuous-Galerkin schemes

Journal of Computational Physics

The Discontinuous Galerkin Method for Two-Dimensional Hyperbolic Problems. Part I: Superconvergence Error Analysis

Journal of Scientific Computing

Minimal Stabilization for Discontinuous Galerkin Finite Element Methods for Hyperbolic Problems

Journal of Scientific Computing

Asymmetric cubature formulas for polynomial integration in the triangle and square

Journal of Computational and Applied Mathematics

A unified framework for the construction of one-step finite volume and discontinuous Galerkin schemes on unstructured meshes

Journal of Computational Physics

Improved Performance for Nodal Spectral Element Operators

International Journal of High Performance Computing Applications

A parallel spectral element method for dynamic three-dimensional nonlinear elasticity problems

Computers and Structures

The Discontinuous Galerkin Method for Two-dimensional Hyperbolic Problems Part II: A Posteriori Error Estimation

Journal of Scientific Computing

Efficient, high accuracy ADER-WENO schemes for hydrodynamics and divergence-free magnetohydrodynamics

Journal of Computational Physics

Singularity-free evaluation of collapsed-coordinate orthogonal polynomials

ACM Transactions on Mathematical Software (TOMS)

On the role of Riemann solvers in Discontinuous Galerkin methods for magnetohydrodynamics

Journal of Computational Physics

Construction of H1-conforming hierarchical shape functions for elements of all shapes and transfinite interpolation

Finite Elements in Analysis and Design

A non-uniform basis order for the discontinuous Galerkin method of the 3D dissipative wave equation with perfectly matched layer

Journal of Computational Physics

From h to p efficiently: Implementing finite and spectral/hp element methods to achieve optimal performance for low- and high-order discretisations

Journal of Computational Physics

Least-squares polynomial approximation on weakly admissible meshes: Disk and triangle

Journal of Computational and Applied Mathematics

Spectral element methods on unstructured meshes: which interpolation points?

Numerical Algorithms

A non-uniform basis order for the discontinuous Galerkin method of the acoustic and elastic wave equations

Applied Numerical Mathematics

A Class of Domain Decomposition Preconditioners for hp-Discontinuous Galerkin Finite Element Methods

Journal of Scientific Computing

An eigen-based high-order expansion basis for structured spectral elements

Journal of Computational Physics

Scalable Direct Vlasov Solver with Discontinuous Galerkin Method on Unstructured Mesh

SIAM Journal on Scientific Computing

A stable interface element scheme for the p-adaptive lifting collocation penalty formulation

Journal of Computational Physics

Well-conditioned Orthonormal Hierarchical $\mathcal{L}_{2}$ Bases on Rn Simplicial Elements

Journal of Scientific Computing

Computing Fekete and Lebesgue points: Simplex, square, disk

Journal of Computational and Applied Mathematics

To CG or to HDG: A Comparative Study

Journal of Scientific Computing

A New Class of High-Order Energy Stable Flux Reconstruction Schemes for Triangular Elements

Journal of Scientific Computing

Boundary concentrated finite elements for optimal boundary control problems of elliptic PDEs

Computational Optimization and Applications

On the generation of symmetric Lebesgue-like points in the triangle

Journal of Computational and Applied Mathematics

Time Implicit High-Order Discontinuous Galerkin Method with Reduced Evaluation Cost

SIAM Journal on Scientific Computing

Bernstein-Bézier Finite Elements of Arbitrary Order and Optimal Assembly Procedures

SIAM Journal on Scientific Computing

Short Note: A comparison of the Discontinuous-Galerkin- and Spectral-Difference-Method on triangulations using PKD polynomials

Journal of Computational Physics

Efficient implementation of ADER schemes for Euler and magnetohydrodynamical flows on structured meshes - Speed comparisons with Runge-Kutta methods

Journal of Computational Physics

Optimized code generation for finite element local assembly using symbolic manipulation

ACM Transactions on Mathematical Software (TOMS)

Energy stable flux reconstruction schemes for advection-diffusion problems on triangles

Journal of Computational Physics

Fast time implicit-explicit discontinuous Galerkin method for the compressible Navier-Stokes equations

Journal of Computational Physics

Vectorized OpenCL implementation of numerical integration for higher order finite elements

Computers & Mathematics with Applications

A new triangular spectral element method I: implementation and analysis on a triangle

Numerical Algorithms

High-order spectral/hp element discretisation for reaction-diffusion problems on surfaces: Application to cardiac electrophysiology

Journal of Computational Physics

On the stability of the boundary trace of the polynomial L2-projection on triangles and tetrahedra

Computers & Mathematics with Applications

Numerical integration on GPUs for higher order finite elements

Computers & Mathematics with Applications