<?xml version="1.0" encoding="utf-8" ?>
<NEKTAR>
    <EXPANSIONS>
        <E COMPOSITE="C[1]" NUMMODES="5" TYPE="MODIFIED" FIELDS="u" />
        <E COMPOSITE="C[2]" NUMMODES="5" TYPE="MODIFIED" FIELDS="u" />
        <E COMPOSITE="C[3]" NUMMODES="5" TYPE="MODIFIED" FIELDS="u" />
    </EXPANSIONS>
    <CONDITIONS>
        <PARAMETERS>
            <P> Lambda  = 2.5  </P>
        </PARAMETERS>

        <SOLVERINFO>
            <I PROPERTY="EQTYPE"                VALUE="Helmholtz"   />
            <I PROPERTY="Projection"            VALUE="Continuous"       />
        </SOLVERINFO>

        <VARIABLES>
            <V ID="0"> u </V>
        </VARIABLES>

        <BOUNDARYREGIONS>
            <B ID="0"> C[100] </B>
            <B ID="1"> C[200] </B>
            <B ID="2"> C[300] </B>
            <B ID="3"> C[400] </B>
        </BOUNDARYREGIONS>

        <BOUNDARYCONDITIONS>
            <REGION REF="0">
                <N VAR="u" VALUE="-PI*cos(PI*x)*sin(PI*y)" />
            </REGION>
            <REGION REF="1">
                <D VAR="u" VALUE="cos(PI*x)*cos(PI*y)" />
            </REGION>
            <REGION REF="2">
                <N VAR="u" VALUE="PI*cos(PI*x)*sin(PI*y)" />
            </REGION>
            <REGION REF="3">
                <D VAR="u" VALUE="cos(PI*x)*cos(PI*y)" />
            </REGION>
        </BOUNDARYCONDITIONS>

        <FUNCTION NAME="Forcing">
            <E VAR="u" VALUE="-(Lambda + 2*PI*PI)*cos(PI*x)*cos(PI*y)" />
        </FUNCTION>

        <FUNCTION NAME="ExactSolution">
            <E VAR="u"  VALUE="cos(PI*x)*cos(PI*y)" />
        </FUNCTION>

    </CONDITIONS>
</NEKTAR>
