Finite element Runge-Kutta discretizations of porous medium type equations

• In this paper we analyze the convergence properties of full discretizations of a class of generalized porous medium equations. For the spatial and time discretizations, we use continuous piecewise linear finite elements and algebraically stable Runge-Kutta methods, respectively. We prove our convergence result without any assumption on the spatial regularity. It is shown that, under a certain stability assumption, the temporal order of convergence is given by the stage order of the method, whereas the spatial order is essentially one. Numerical experiments illustrate our stability assumption and the convergence result.

Ämnesord

TEKNIK OCH TEKNOLOGIER  -- Elektroteknik och elektronik (hsv//swe)

ENGINEERING AND TECHNOLOGY  -- Electrical Engineering, Electronic Engineering, Information Engineering (hsv//eng)

Nyckelord

Runge-Kutta time discretization

high order convergence in time

degenerate parabolic problems

porous medium equation

Publikations- och innehållstyp

art (ämneskategori)

ref (ämneskategori)