Use solidity ecrecover with signature calculated with eth_sign

ercevocer.js

// Change accountToSignWith to the address of your account.

var Web3 = require('web3');
var web3 = new Web3();

web3.setProvider(new web3.providers.HttpProvider('http://localhost:8545'));

var accountToSignWith = '0xbedcf417ff2752d996d2ade98b97a6f0bef4beb9';
var message = 'Lorem ipsum dolor sit amet, consectetur adipiscing elit. Tubulum fuisse, qua illum, cuius is condemnatus est rogatione, P. Eaedem res maneant alio modo.'

var contractSource = `
contract SignAndVerifyExample {
    function RecoverAddress(bytes32 msgHash, uint8 v, bytes32 r, bytes32 s) constant returns (address) {
        return ecrecover(msgHash, v, r, s);
    }
}
`;

var contractABI = [{"constant":true,"inputs":[{"name":"msgHash","type":"bytes32"},{"name":"v","type":"uint8"},{"name":"r","type":"bytes32"},{"name":"s","type":"bytes32"}],"name":"RecoverAddress","outputs":[{"name":"","type":"address"}],"payable":false,"type":"function"}];
var contractAddress = '0x5481c0fe170641bd2e0ff7f04161871829c1902d'; // on Ropsten and Rinkeby

var signAndVerifyContract = web3.eth.contract(contractABI).at(contractAddress);

// eth_sign calculated the signature over keccak256("\x19Ethereum Signed Message:\n" + len(givenMessage) + givenMessage)))
// this gives context to a signature and prevents signing of transactions.
function messageHash(msg) {
	return web3.sha3('\x19Ethereum Signed Message:\n' + msg.length + msg);
}

function verifyHandler(err, address) {
	if (!err) {
		console.log('Recovered address:', address);
		console.log('  Address matched:', accountToSignWith === address);
	} else {
		console.err('Could not recover address:', err);
	}
}

function signHandler(err, signature) {
	if (!err) {
		console.log('Signature:', signature);
		signature = signature.substr(2);
		r = '0x' + signature.substr(0, 64);
		s = '0x' + signature.substr(64, 64);
		v = '0x' + signature.substr(128, 2)
				
		console.log('        r:', r)
		console.log('        s:', s)
		console.log('        v:', v)
		console.log();
				
		signAndVerifyContract.RecoverAddress(messageHash(message), v, r, s, verifyHandler);
	} else {
		console.error('Coult not sign message:', err);
	}
}

console.log('  Message to sign:', message);
console.log('Sign with account:', accountToSignWith);
console.log();

var messageHex = '0x' + Buffer.from(message).toString('hex');
web3.eth.sign(accountToSignWith, messageHex, signHandler);