Abstract
An extension of the familiar Taylor-Galerkin method to arbitrary h- p spatial approximations is proposed. Boundary conditions are analyzed and a linear stability result for arbitrary meshes is given, showing the unconditional stability for the parameter of implicitness α ⩾ 0.5. The wedge and blunt body problems are solved with both linear, quadratic and cubic elements and h-adaptivity, showing the feasibility of higher orders of approximation for problems with shocks.
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