A New Multiscale Discontinuous Galerkin Method for a Class of Second-Order Equations with Oscillatory Solutions in Two-Dimensional Space
Book Chapter
Dong, B, Wang, W. (2023). A New Multiscale Discontinuous Galerkin Method for a Class of Second-Order Equations with Oscillatory Solutions in Two-Dimensional Space
. 137 239-250. 10.1007/978-3-031-20432-6_14
Dong, B, Wang, W. (2023). A New Multiscale Discontinuous Galerkin Method for a Class of Second-Order Equations with Oscillatory Solutions in Two-Dimensional Space
. 137 239-250. 10.1007/978-3-031-20432-6_14
We develop a new high-order multiscale discontinuous Galerkin (DG) method for a class of second-order equations with oscillatory solutions in two-dimensional space. The solutions of these equations mainly oscillate in one direction, so we use non-polynomial basis functions in that direction and polynomial basis in the other direction. Numerically we observe that the method converges on coarse meshes where traditional DG methods fail. On fine meshes, our method achieves optimal higher-order convergence and the errors are several magnitudes smaller than those of traditional DG methods.
