A conservative implicit multirate method for hyperbolic problems

A Conservative Front Tracking Method for Hyperbolic Conservation Laws

A stable hybrid method for hyperbolic problems

A stable hybrid method for hyperbolic problems that combines the unstructured finite volume method with high-order finite difference methods has been developed. The coupling procedure is based on energy estimates and stability can be guaranteed. Numerical calculations verify that the hybrid method is efficient and accurate.

Comparison of two Conservative Schemes for Hyperbolic Interface Problems

We recall two conservative schemes recently proposed for the numerical solution of hyperbolic interface problems. Then, we compare the two schemes on a piston problem and a shock tube problem.

Explicit / Implicit Conservative Galerkin Domain Decomposition Procedures for Parabolic Problems

Several domain decomposition methods for approximating solutions of parabolic problems are given. These methods rely on implicit Galerkin procedures in the subdomains and explicit flux calculation on the inter-domain boundaries. The procedures are conservative both in the subdomains and across inter-domain boundaries. A priori error bounds and experimental results are presented.

An Unconditionally Stable Implicit High-Order Domain Decomposition Method for Two-Dimensional Second-Order Hyperbolic Problems

A new three-level implicit prediction/correction method of second order is proposed for the two-dimensional linear second-order hyperbolic equation utt+a(x, y, t)ut+b(x, y, t)u = c(x, y, t)uxx+d(x, y, t)uyy+ f(x, y, t) subject to initial and boundary conditions. The domain decomposition technique has been incorporated in the method. Numerical experiments illustrates that the method is accurate,...