For a given triangulation Δ of a region R of interest, let S_8~2(Δ): = {s∈C^2(R): s|_1∈P_8,l∈Δ} be the space of all splines of degree 8 and smoothness 2, where t denotes any triangle of Δ and P_8 the space of ...For a given triangulation Δ of a region R of interest, let S_8~2(Δ): = {s∈C^2(R): s|_1∈P_8,l∈Δ} be the space of all splines of degree 8 and smoothness 2, where t denotes any triangle of Δ and P_8 the space of polynomials of total degree≤8. Furthermore, let S_8~2(Δ):={s∈S_8~3(Δ):s∈C^3 at v, v∈Δ} be a super spline subspace of S_8~2(Δ). We construel a collection of locally supported splines in S_8~2(Δ) which can be used to achieve lhe full approximation order of S_8~2(Δ) and its cardinalily is less than the di- mension of super spline space space S_8~2(Δ).展开更多
文摘For a given triangulation Δ of a region R of interest, let S_8~2(Δ): = {s∈C^2(R): s|_1∈P_8,l∈Δ} be the space of all splines of degree 8 and smoothness 2, where t denotes any triangle of Δ and P_8 the space of polynomials of total degree≤8. Furthermore, let S_8~2(Δ):={s∈S_8~3(Δ):s∈C^3 at v, v∈Δ} be a super spline subspace of S_8~2(Δ). We construel a collection of locally supported splines in S_8~2(Δ) which can be used to achieve lhe full approximation order of S_8~2(Δ) and its cardinalily is less than the di- mension of super spline space space S_8~2(Δ).
