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Accuracy-preserving source term quadrature for third-order edge-based discretization. (English) Zbl 1380.65334
Summary: In this paper, we derive a family of source term quadrature formulas for preserving third-order accuracy of the node-centered edge-based discretization for conservation laws with source terms on arbitrary simplex grids. A three-parameter family of source term quadrature formulas is derived, and as a subset, a one-parameter family of economical formulas is identified that does not require second derivatives of the source term. Among the economical formulas, a unique formula is then derived that does not require gradients of the source term at neighbor nodes, thus leading to a significantly smaller discretization stencil for source terms. All the formulas derived in this paper do not require a boundary closure, and therefore can be directly applied at boundary nodes. Numerical results are presented to demonstrate third-order accuracy at interior and boundary nodes for one-dimensional grids and linear triangular/tetrahedral grids over straight and curved geometries.

65N08 Finite volume methods for boundary value problems involving PDEs
65N50 Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs
EDGE; FUN3D; Premo
Full Text: DOI
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