On spatial adaptivity and interpolation when using the method of lines

The solution of time-dependent partial differential equations with discrete time static remeshing is considered within a method of lines framework. Numerical examples in one and two space dimensions are used to show that spatial interpolation error may have an important impact on the efficiency of integration. Analysis of a simple problem and of the time integration method is used to confirm the experimental results and a computational test for monitoring the impact of this error is derived and tested.