Journal of Computational Physics
Adaptive finite element methods for parabolic problems. I.: a linear model problem
SIAM Journal on Numerical Analysis
Godunov-mixed methods for advective flow problems in one space dimension
SIAM Journal on Numerical Analysis
Godunov-mixed methods for advection-diffusion equations in multidimensions
SIAM Journal on Numerical Analysis
Parallel, adaptive finite element methods for conservation laws
Proceedings of the third ARO workshop on Adaptive methods for partial differential equations
SIAM Journal on Numerical Analysis
Adaptive finite element methods for parabolic problems II: optimal error estimates in L∞L2 and L∞L∞
SIAM Journal on Numerical Analysis
Parallel adaptive hp-refinement techniques for conservation laws
Applied Numerical Mathematics - Special issue on adaptive mesh refinement methods for CFD applications
Journal of Computational Physics
The Runge-Kutta discontinuous Galerkin method for conservation laws V multidimensional systems
Journal of Computational Physics
The Local Discontinuous Galerkin Method for Time-Dependent Convection-Diffusion Systems
SIAM Journal on Numerical Analysis
Journal of Scientific Computing
Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra, 3/e (Undergraduate Texts in Mathematics)
Journal of Scientific Computing
Journal of Scientific Computing
A Superconvergent Local Discontinuous Galerkin Method for Elliptic Problems
Journal of Scientific Computing
Hi-index | 0.00 |
In this manuscript we present a superconvergent discontinuous Galerkin method equipped with an element residual error estimator applied to scalar first-order hyperbolic problems using tetrahedral meshes. We present a local error analysis to derive a discontinuous Galerkin orthogonality condition for the leading term of the discretization error and establish new superconvergence points, lines and surfaces. We also derive new basis functions spanning the error and propose an implicit error estimation procedure by solving a local problem on each tetrahedron. The DG method combined with the a posteriori error estimation procedure yields both accurate error estimates and $$O(h^{p+2})$$O(hp+2) superconvergent solutions. Computations validate our theory.