12 citations · 27 across the 4 of their papers we have counts for
5 papers
A Fully Discrete, Mass-Conservative Adaptive Discontinuous Spectral-Element Method for the One-Dimensional Richards Equation in Mixed Form
Tristan Montoya, Raymond J. Spiteri
We present and analyze a spatially and temporally adaptive high-order method for the one-dimensional Richards equation describing vertical water transport in unsaturated soil, with…
Entropy-Stable Discontinuous Spectral-Element Methods for the Spherical Shallow Water Equations in Covariant Form
Tristan Montoya, Andrés M. Rueda-Ramírez, Gregor J. Gassner
We introduce discontinuous spectral-element methods of arbitrary order that are well balanced, conservative of mass, and conservative or dissipative of total energy (i.e., a mathem…
Efficient Entropy-Stable Discontinuous Spectral-Element Methods Using Tensor-Product Summation-by-Parts Operators on Triangles and Tetrahedra
Tristan Montoya, David W. Zingg
We present a new class of efficient and robust discontinuous spectral-element methods of arbitrary order for nonlinear hyperbolic systems of conservation laws on curved triangular…
Efficient Tensor-Product Spectral-Element Operators with the Summation-by-Parts Property on Curved Triangles and Tetrahedra
Tristan Montoya, David W. Zingg
We present an extension of the summation-by-parts (SBP) framework to tensor-product spectral-element operators in collapsed coordinates. The proposed approach enables the construct…
A unifying algebraic framework for discontinuous Galerkin and flux reconstruction methods based on the summation-by-parts property
Tristan Montoya, David W. Zingg
We propose a unifying framework for the matrix-based formulation and analysis of discontinuous Galerkin (DG) and flux reconstruction (FR) methods for conservation laws on general u…