Stability analysis and error estimates of a class of spectral volume methods for hyperbolic equations over unstructured quadrilateral meshes

In this paper, a stable and arbitrary high-order spectral volume (SV) method is proposed for solving linear hyperbolic conservation laws on unstructured quadrilateral meshes. The SV scheme is constructed with subdivision points being zeros of a class of parameterized polynomials. A unified proof for the L 2 stability of the SV method is provided under conditions that the parameter c > − 1/ k ( k +1) and the underlying mesh is an h 1+ γ , γ ≥ 1 parallelogram mesh. The optimal a priori error estimate of SV methods is established. Numerical experiments are presented to verify all theoretical findings.