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+ <meta name="author" content="Ralf Hartmann <Ralf Hartmann@iwr.uni-heidelberg.de>">
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+
+
+<H3>Abstract:</H3>
+<DIR>
+We consider the <em>a posteriori</em> error analysis
+and adaptive mesh design for discontinuous Galerkin finite
+element approximations to systems of nonlinear
+hyperbolic conservation laws.
+In particular, we discuss the question of error estimation for general
+linear and nonlinear functionals of the solution; typical examples
+include the
+outflow flux, local average and pointwise value, as well as the lift
+and drag coefficients of a body immersed in an inviscid fluid.
+By employing a duality argument, we derive so-called weighted or Type I
+<em>a posteriori</em> error bounds; in these error estimates
+the element--residuals are multiplied by local weights involving
+the solution of a certain dual problem. Based on these <em>a posteriori</em>
+bounds, we design and implement the corresponding adaptive algorithm
+to ensure efficient and reliable control of the error in the
+computed functional. The theoretical results are illustrated by a series of
+numerical experiments. In particular, we demonstrate the superiority
+of the proposed approach over standard mesh refinement algorithms which employ
+<em>ad hoc</em> error indicators.
+
+</DIR>
+<P>
+<BR><HR>
+<ADDRESS>
+<I>Ralf Hartmann</I>
+<BR><I>2000-05-04</I>
+</ADDRESS>
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+</HTML>