论文标题
关于可压缩欧拉方程的残留分布方案通过耗散弱解的收敛性
On the convergence of residual distribution schemes for the compressible Euler equations via dissipative weak solutions
论文作者
论文摘要
在这项工作中，我们证明了残余分布方案与Euler方程耗散弱解的收敛性。我们需要确保剩余分布方案实现了维护属性的基本结构，例如密度和内部能量的阳性。因此，剩余分布方案导致欧拉方程的一致稳定近似。我们的结果可以看作是将松弛的含量等效定理与非线性问题的概括，即一致性加稳定性等效于收敛。
In this work, we prove the convergence of residual distribution schemes to dissipative weak solutions of the Euler equations. We need to guarantee that the residual distribution schemes are fulfilling the underlying structure preserving properties such as positivity of density and internal energy. Consequently, the residual distribution schemes lead to a consistent and stable approximation of the Euler equations. Our result can be seen as a generalization of the Lax-Richtmyer equivalence theorem to nonlinear problems that consistency plus stability is equivalent to convergence.
