Efficient implementation of essentially non-oscillatory shock-capturing schemes
Journal of Computational Physics
Introduction to numerical analysis: 2nd edition
Introduction to numerical analysis: 2nd edition
Parallel, adaptive finite element methods for conservation laws
Proceedings of the third ARO workshop on Adaptive methods for partial differential equations
Why nonconservative schemes converge to wrong solutions: error analysis
Mathematics of Computation
Nonlinearly stable compact schemes for shock calculations
SIAM Journal on Numerical Analysis
The continuous Galerkin method is locally conservative
Journal of Computational Physics
Spectral methods for hyperbolic problems
Journal of Computational and Applied Mathematics - Special issue on numerical analysis 2000 Vol. VII: partial differential equations
On Monotonicity of Difference Schemes for Computational Physics
SIAM Journal on Scientific Computing
Variable-order finite elements and positivity preservation for hyperbolic PDEs
Applied Numerical Mathematics - Special issue: Workshop on innovative time integrators for PDEs
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The positivity preserving approach of Berzins is generalized by using a derivation based on bounded polynomial approximations and order selection. The approach is extended from the B-spline based methods used previously to the use of more conventional continuous Galerkin elements. The conditions relating to positivity preservation are considered and a numerical example used to demonstrate the performance of the method on a model advection equation problem.