Journal of Scientific Computing
Journal of Computational Physics
Discontinuous Galerkin spectral element approximations on moving meshes
Journal of Computational Physics
Refinement and Connectivity Algorithms for Adaptive Discontinuous Galerkin Methods
SIAM Journal on Scientific Computing
SIAM Journal on Scientific Computing
Boundary states at reflective moving boundaries
Journal of Computational Physics
Optimal Gegenbauer quadrature over arbitrary integration nodes
Journal of Computational and Applied Mathematics
A Spectral Element Framework for Option Pricing Under General Exponential Lévy Processes
Journal of Scientific Computing
High-Order Local Time Stepping on Moving DG Spectral Element Meshes
Journal of Scientific Computing
Dispersive behaviour of high order finite element schemes for the one-way wave equation
Journal of Computational Physics
Journal of Computational Physics
The Estimation of Truncation Error by $$\tau $$-Estimation for Chebyshev Spectral Collocation Method
Journal of Scientific Computing
ALE-DGSEM approximation of wave reflection and transmission from a moving medium
Journal of Computational Physics
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This book offers a systematic and self-contained approach to solvepartial differential equations numerically using single and multidomain spectralmethods. It contains detailed algorithms in pseudocode for the applicationof spectral approximations to both one and two dimensional PDEsof mathematical physics describing potentials,transport, and wave propagation. David Kopriva, a well-known researcherin the field with extensive practical experience, shows how only a fewfundamental algorithms form the building blocks of any spectral code, evenfor problems with complex geometries. The book addresses computationaland applications scientists, as it emphasizes thepractical derivation and implementation of spectral methods over abstract mathematics. It is divided into two parts: First comes a primer on spectralapproximation and the basic algorithms, including FFT algorithms, Gaussquadrature algorithms, and how to approximate derivatives. The secondpart shows how to use those algorithms to solve steady and time dependent PDEs in one and two space dimensions. Exercises and questions at theend of each chapter encourage the reader to experiment with thealgorithms.